{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,7]],"date-time":"2025-11-07T13:40:50Z","timestamp":1762522850477,"version":"build-2065373602"},"reference-count":75,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2023,8,18]],"date-time":"2023-08-18T00:00:00Z","timestamp":1692316800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100018227","name":"National Research Foundation of Ukraine","doi-asserted-by":"publisher","award":["2020.02\/0025"],"award-info":[{"award-number":["2020.02\/0025"]}],"id":[{"id":"10.13039\/100018227","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In the paper, we study various countably generated algebras of entire analytic functions on complex Banach spaces and their homomorphisms. Countably generated algebras often appear as algebras of symmetric analytic functions on Banach spaces with respect to a group of symmetries, and are interesting for their possible applications. Some conditions of the existence of topological isomorphisms between such algebras are obtained. We construct a class of countably generated algebras, where all normalized algebraic bases are equivalent. On the other hand, we find non-isomorphic classes of such algebras. In addition, we establish the conditions of the hypercyclicity of derivations in countably generated algebras of entire analytic functions of the bounded type. We use methods from the theory of analytic functions of several variables, the theory of commutative Fr\u00e9chet algebras, and the theory of linear dynamical systems.<\/jats:p>","DOI":"10.3390\/axioms12080798","type":"journal-article","created":{"date-parts":[[2023,8,18]],"date-time":"2023-08-18T10:28:48Z","timestamp":1692354528000},"page":"798","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Countably Generated Algebras of Analytic Functions on Banach Spaces"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2283-1879","authenticated-orcid":false,"given":"Zoriana","family":"Novosad","sequence":"first","affiliation":[{"name":"Department of Higher Mathematics and Quantitative Methods 10, Lviv University of Trade and Economics, Tuhan-Baranovsky Street, 79005 Lviv, Ukraine"}]},{"given":"Svitlana","family":"Vasylyshyn","sequence":"additional","affiliation":[{"name":"Faculty of Mathematics and Computer Science, Vasyl Stefanyk Precarpathian National University, 57 Shevchenka Street, 76018 Ivano-Frankivsk, Ukraine"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5554-4342","authenticated-orcid":false,"given":"Andriy","family":"Zagorodnyuk","sequence":"additional","affiliation":[{"name":"Faculty of Mathematics and Computer Science, Vasyl Stefanyk Precarpathian National University, 57 Shevchenka Street, 76018 Ivano-Frankivsk, Ukraine"}]}],"member":"1968","published-online":{"date-parts":[[2023,8,18]]},"reference":[{"key":"ref_1","unstructured":"Kajiwara, J., Li, Z., and Shon, K.H. (2000). Finite or Infinite Dimensional Complex Analysis, CRC Press."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"213","DOI":"10.1007\/BF01456881","article-title":"Spectrum and envelope of holomorphy for infinite dimensional Riemann domains","volume":"263","author":"Schottenloher","year":"1983","journal-title":"Math. Ann."},{"key":"ref_3","first-page":"51","article-title":"Spectra of algebras of analytic functions on a Banach space","volume":"415","author":"Aron","year":"1991","journal-title":"J. Reine Angew. Math."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"673","DOI":"10.4153\/CJM-1995-035-1","article-title":"Weak-star continuous analytic functions","volume":"47","author":"Aron","year":"1995","journal-title":"Can. J. Math."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"543","DOI":"10.1090\/S0002-9947-96-01553-X","article-title":"Regularity and algebras of analytic functions in infinite dimensions","volume":"348","author":"Aron","year":"1996","journal-title":"Trans. Am. Math. Soc."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"2559","DOI":"10.1090\/S0002-9939-06-08260-8","article-title":"Spectra of algebras of entire functions on Banach spaces","volume":"134","author":"Zagorodnyuk","year":"2006","journal-title":"Proc. Am. Math. Soc."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Dineen, S. (1999). Complex Analysis on Infinite Dimensional Spaces, Springer.","DOI":"10.1007\/978-1-4471-0869-6"},{"key":"ref_8","first-page":"243","article-title":"On the weak continuity of the polynomial functionals on the space c0","volume":"21","author":"Bogdanowicz","year":"1957","journal-title":"Bull. Acad. Polon. Sci."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"292","DOI":"10.1007\/s000130050571","article-title":"Ideals of holomorphic functions on Tsirelson\u2019s space","volume":"76","author":"Mujica","year":"2001","journal-title":"Arch. Math."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"607","DOI":"10.1016\/j.aim.2004.10.018","article-title":"Homomorphisms and composition operators on algebras of analytic functions of bounded type","volume":"197","author":"Carando","year":"2005","journal-title":"Adv. Math."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"165","DOI":"10.1090\/conm\/561\/11114","article-title":"On the spectra of algebras of analytic functions","volume":"561","author":"Carando","year":"2012","journal-title":"Contemp. Math."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"447","DOI":"10.1006\/jmaa.2000.6762","article-title":"The spectrum of analytic mappings of bounded type","volume":"245","author":"Maestre","year":"2000","journal-title":"J. Math. Anal. Appl."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"393","DOI":"10.1016\/S0019-3577(99)80031-7","article-title":"The spectra of some algebras of analytic mappings","volume":"10","author":"Moraes","year":"1999","journal-title":"Indag. Math."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"269","DOI":"10.1016\/S0019-3577(07)80022-X","article-title":"Spectra of algebras of holomorphic functions of bounded type","volume":"18","author":"Vieira","year":"2007","journal-title":"Indag. Math."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1112\/S0024609302001431","article-title":"Algebra of symmetric holomorphic functions on \u2113p","volume":"35","author":"Alencar","year":"2003","journal-title":"Bull. Lond. Math. Soc."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"779","DOI":"10.1112\/blms\/bdw043","article-title":"Group-symmetric holomorphic functions on a Banach space","volume":"48","author":"Aron","year":"2016","journal-title":"Bull. Lond. Math. Soc."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"125","DOI":"10.1017\/S0013091509001655","article-title":"Some algebras of symmetric analytic functions and their spectra","volume":"55","author":"Chernega","year":"2012","journal-title":"Proc. Edinb. Math. Soc."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"569","DOI":"10.1016\/j.jmaa.2012.04.087","article-title":"The convolution operation on the spectra of algebras of symmetric analytic functions","volume":"395","author":"Chernega","year":"2012","journal-title":"J. Math. Anal. Appl."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"743","DOI":"10.1017\/S0308210516000287","article-title":"The algebra of symmetric analytic functions on L\u221e","volume":"147","author":"Galindo","year":"2017","journal-title":"Proc. R. Soc. Edinb. Sect. A Math."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"56","DOI":"10.1007\/s13398-020-00791-w","article-title":"Analytic structure on the spectrum of the algebra of symmetric analytic functions on L\u221e","volume":"114","author":"Galindo","year":"2020","journal-title":"RACSAM"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"393","DOI":"10.1007\/s12220-017-9825-0","article-title":"Separation theorems for group invariant polynomials","volume":"28","author":"Aron","year":"2018","journal-title":"J. Geom. Anal."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Bandura, A., Kravtsiv, V., and Vasylyshyn, T. (2022). Algebraic Basis of the Algebra of All Symmetric Continuous Polynomials on the Cartesian Product of \u2113p-Spaces. Axioms, 11.","DOI":"10.3390\/axioms11020041"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"207","DOI":"10.5565\/PUBLMAT6612209","article-title":"Group-invariant separating polynomials on a Banach space","volume":"66","author":"Jung","year":"2022","journal-title":"Publ. Mat."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"204","DOI":"10.15330\/ms.50.2.204-210","article-title":"Note on separately symmetric polynomials on the Cartesian product of \u2113p","volume":"50","author":"Jawad","year":"2018","journal-title":"Mat. Stud."},{"key":"ref_25","first-page":"4947925","article-title":"On algebraic basis of the algebra of symmetric polynomials on \u2113p(Cn)","volume":"2017","author":"Kravtsiv","year":"2017","journal-title":"J. Funct. Spaces"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"164","DOI":"10.1007\/s40879-018-0268-3","article-title":"Symmetric polynomials on (Lp)n","volume":"6","author":"Vasylyshyn","year":"2020","journal-title":"Eur. J. Math."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"93","DOI":"10.15330\/ms.50.1.93-104","article-title":"Symmetric polynomials on the Cartesian power of Lp on the semi-axis","volume":"50","author":"Vasylyshyn","year":"2018","journal-title":"Mat. Stud."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"340","DOI":"10.15330\/cmp.13.2.340-351","article-title":"Algebras of symmetric analytic functions on Cartesian powers of Lebesgue integrable in a power p\u2208[1,+\u221e) functions","volume":"13","author":"Vasylyshyn","year":"2021","journal-title":"Carpathian Math. Publ."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"71","DOI":"10.30970\/ms.52.1.71-85","article-title":"The algebra of symmetric polynomials on (L\u221e)n","volume":"52","author":"Vasylyshyn","year":"2019","journal-title":"Mat. Stud."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"125977","DOI":"10.1016\/j.jmaa.2021.125977","article-title":"Symmetric analytic functions on the Cartesian power of the complex Banach space of Lebesgue measurable essentially bounded functions on [0,1]","volume":"509","author":"Vasylyshyn","year":"2022","journal-title":"J. Math. Anal. Appl."},{"key":"ref_31","first-page":"381","article-title":"Continuous symmetric 3-homogeneous polynomials on spaces of Lebesgue measurable essentially bounded functions","volume":"24","author":"Vasylyshyn","year":"2018","journal-title":"Methods Funct. Anal. Topol."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"69","DOI":"10.30970\/ms.58.1.69-81","article-title":"Spectra of algebras of block-symmetric analytic functions of bounded type","volume":"58","author":"Zagorodnyuk","year":"2022","journal-title":"Mat. Stud."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"311","DOI":"10.15330\/cmp.11.2.311-320","article-title":"Spectra of Some Algebras of Entire Functions of Bounded Type, Generated by a Sequence of Polynomials","volume":"11","author":"Halushchak","year":"2019","journal-title":"Carpathian Math. Publ."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"106","DOI":"10.30970\/ms.56.1.106-112","article-title":"Isomorphisms of some algebras of analytic functions of bounded type on Banach spaces","volume":"56","author":"Halushchak","year":"2021","journal-title":"Mat. Stud."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"104","DOI":"10.15330\/cmp.15.1.104-119","article-title":"Spectra of Algebras of Analytic Functions, Generated by Sequences of Polynomials on Banach Spaces, and Operations on Spectra","volume":"15","author":"Vasylyshyn","year":"2023","journal-title":"Carpathian Math. Publ."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"651","DOI":"10.1007\/s13163-018-0261-x","article-title":"Algebras of symmetric holomorphic functions of several complex variables","volume":"31","author":"Aron","year":"2018","journal-title":"Rev. Mat. Complut."},{"key":"ref_37","unstructured":"Mujica, J. (1986). Complex Analysis in Banach Spaces, North-Holland."},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Bayart, F., and Matheron, E. (2009). Dynamics of Linear Operators, Cambridge University Press.","DOI":"10.1017\/CBO9780511581113"},{"key":"ref_39","doi-asserted-by":"crossref","unstructured":"Grosse-Erdmann, K.G., and Peris Manguillot, A. (2011). Linear Chaos, Springer.","DOI":"10.1007\/978-1-4471-2170-1"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"483","DOI":"10.1016\/S0019-3577(09)80021-9","article-title":"Behavior of entire functions on balls in a Banach space","volume":"20","author":"Ansemil","year":"2009","journal-title":"Indag. Math."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"383","DOI":"10.2977\/prims\/1241553124","article-title":"Representation of spaces of entire functions on Banach spaces","volume":"45","author":"Ansemil","year":"2009","journal-title":"Publ. Res. Inst. Math. Sci."},{"key":"ref_42","first-page":"473","article-title":"D\u00e9monstration d\u2019un th\u00e9or\u00e8me \u00e9l\u00e9mentaire sur les fonctions enti\u00e8res","volume":"189","author":"Birkhoff","year":"1929","journal-title":"C. R. Acad. Sci. Paris"},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"229","DOI":"10.1016\/0022-1236(91)90078-J","article-title":"Operators with dense, invariant, cyclic vector manifolds","volume":"98","author":"Godefroy","year":"1991","journal-title":"J. Funct. Anal."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"39","DOI":"10.1090\/conm\/232\/03382","article-title":"Hypercyclic differentiation operators","volume":"232","author":"Aron","year":"1999","journal-title":"Contemp. Math."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"153","DOI":"10.1007\/s40879-019-00390-z","article-title":"Continuity and hypercyclicity of composition operators on algebras of symmetric analytic functions on Banach spaces","volume":"6","author":"Chernega","year":"2020","journal-title":"Eur. J. Math."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1007\/s00013-007-2043-4","article-title":"Polynomial automorphisms and hypercyclic operators on spaces of analytic functions","volume":"89","author":"Novosad","year":"2007","journal-title":"Arch. Math."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"3","DOI":"10.24033\/bsmf.1862","article-title":"A Hahn-Banach extension theorem for analytic mappings","volume":"106","author":"Aron","year":"1978","journal-title":"Bull. Soc. Math. Fr."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"351","DOI":"10.1090\/S0002-9939-1989-0947313-8","article-title":"A theorem on polynomial-star approximation","volume":"106","author":"Davie","year":"1989","journal-title":"Proc. Am. Math. Soc."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"681","DOI":"10.1112\/S0024610799007164","article-title":"Symmetric polynomials on rearrangement-invariant function spaces","volume":"59","author":"Gonzalo","year":"1999","journal-title":"J. Lond. Math. Soc."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"255","DOI":"10.1070\/SM1973v021n02ABEH002016","article-title":"On polynomial approximation of functions on Hilbert space","volume":"21","author":"Nemirovskii","year":"1973","journal-title":"Mat. USSR-Sb."},{"key":"ref_51","doi-asserted-by":"crossref","unstructured":"Macdonald, I.G. (1997). Symmetric Functions and Orthogonal Polynomials, AMS.","DOI":"10.1090\/ulect\/012"},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1006\/jmaa.1996.0322","article-title":"Multilinear forms, subsymmetric polynomials, and spreading models on Banach spaces","volume":"202","author":"Gonzalo","year":"1996","journal-title":"J. Math. Anal. Appl."},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"1003","DOI":"10.1007\/s11856-015-1155-y","article-title":"Erratum to: \u201cPolynomial algebras on classical Banach spaces\u201d","volume":"207","author":"Johanis","year":"2015","journal-title":"Isr. J. Math."},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"209","DOI":"10.1007\/BF02773469","article-title":"Polynomial algebras on classical Banach Spaces","volume":"106","year":"1998","journal-title":"Isr. J. Math."},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"38","DOI":"10.1007\/s10958-015-2647-3","article-title":"A semiring in the spectrum of the algebra of symmetric analytic functions in the space \u21131","volume":"212","author":"Chernega","year":"2016","journal-title":"J. Math. Sci."},{"key":"ref_56","doi-asserted-by":"crossref","unstructured":"Jawad, F., and Zagorodnyuk, A. (2019). Supersymmetric polynomials on the space of absolutely convergent series. Symmetry, 11.","DOI":"10.3390\/sym11091111"},{"key":"ref_57","first-page":"251","article-title":"Frobenius-Schur Functions","volume":"Volume 210","author":"Joseph","year":"2003","journal-title":"Studies in Memory of Issai Schur. Progress in Mathematics"},{"key":"ref_58","doi-asserted-by":"crossref","first-page":"336","DOI":"10.1016\/j.jalgebra.2018.10.003","article-title":"On rings of supersymmetric polynomials","volume":"517","author":"Sergeev","year":"2019","journal-title":"J. Algebra"},{"key":"ref_59","doi-asserted-by":"crossref","first-page":"439","DOI":"10.1016\/0021-8693(85)90115-2","article-title":"A Characterization of Supersymmetric Polynomials","volume":"95","author":"Stembridge","year":"1985","journal-title":"J. Algebra"},{"key":"ref_60","doi-asserted-by":"crossref","unstructured":"Vasylyshyn, T., and Zhyhallo, K. (2022). Entire Symmetric Functions on the Space of Essentially Bounded Integrable Functions on the Union of Lebesgue-Rohlin Spaces. Axioms, 11.","DOI":"10.3390\/axioms11090460"},{"key":"ref_61","doi-asserted-by":"crossref","first-page":"89","DOI":"10.15330\/cmp.11.1.89-95","article-title":"Algebraic basis of the algebra of block-symmetric polynomials on \u21131\u2295\u2113\u221e","volume":"11","author":"Kravtsiv","year":"2019","journal-title":"Carpathian Math. Publ."},{"key":"ref_62","doi-asserted-by":"crossref","first-page":"17","DOI":"10.15330\/cmp.12.1.17-22","article-title":"Analogues of the Newton formulas for the block-symmetric polynomials","volume":"12","author":"Kravtsiv","year":"2020","journal-title":"Carpathian Math. Publ."},{"key":"ref_63","doi-asserted-by":"crossref","first-page":"206","DOI":"10.30970\/ms.53.2.206-211","article-title":"Zeros of block-symmetric polynomials on Banach spaces","volume":"53","author":"Kravtsiv","year":"2020","journal-title":"Mat. Stud."},{"key":"ref_64","doi-asserted-by":"crossref","unstructured":"Zagorodnyuk, A., and Hihliuk, A. (2021). Entire analytic functions of unbounded type on Banach spaces and their lineability. Axioms, 10.","DOI":"10.1063\/5.0114853"},{"key":"ref_65","first-page":"113","article-title":"Uniqueness of topology for commutative semisimple F-algebras","volume":"29","author":"Carpenter","year":"1971","journal-title":"Proc. Am. Math. Soc."},{"key":"ref_66","doi-asserted-by":"crossref","first-page":"129","DOI":"10.1112\/blms\/10.2.129","article-title":"Automatic continuity: A survey","volume":"10","author":"Dales","year":"1978","journal-title":"Bull. Lond. Math. Soc."},{"key":"ref_67","doi-asserted-by":"crossref","unstructured":"Michael, E.A. (1952). Locally Multiplicatively Convex Topological Algebras, American Mathematical Society. Memoirs of the American Mathematical Society.","DOI":"10.1090\/memo\/0011"},{"key":"ref_68","doi-asserted-by":"crossref","first-page":"500","DOI":"10.2307\/2373390","article-title":"Continuity of derivations in F-algebras","volume":"93","author":"Carpenter","year":"1971","journal-title":"Am. J. Math."},{"key":"ref_69","doi-asserted-by":"crossref","unstructured":"Narici, L., and Beckenstein, E. (2010). Topological Vector Spaces, CRC Press.","DOI":"10.1201\/9781584888673"},{"key":"ref_70","first-page":"211","article-title":"A note on derivations of algebras of analytic functions","volume":"297","author":"Becker","year":"1978","journal-title":"J. Reine Angew. Math."},{"key":"ref_71","doi-asserted-by":"crossref","first-page":"237","DOI":"10.1016\/S1385-7258(89)80001-0","article-title":"Derivations on algebras of holomorphic functions","volume":"92","author":"Brummelhuis","year":"1989","journal-title":"Indag. Math."},{"key":"ref_72","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1016\/S1385-7258(88)80027-1","article-title":"An application of Nienhuys-Thiemann\u2019s theorem to ring derivations on H(G)","volume":"50","author":"Nandakumar","year":"1988","journal-title":"Indag. Math."},{"key":"ref_73","doi-asserted-by":"crossref","unstructured":"Rudin, W. (2008). Function Theory in the Unit Ball of Cn, Springer. Reprint of the 1980 Edition. Classics in Mathematics.","DOI":"10.1007\/978-3-540-68276-9"},{"key":"ref_74","doi-asserted-by":"crossref","first-page":"701","DOI":"10.1512\/iumj.1982.31.31050","article-title":"Proper holomorphic maps and finite reflection groups","volume":"31","author":"Rudin","year":"1982","journal-title":"Indiana Univ. Math. J."},{"key":"ref_75","doi-asserted-by":"crossref","first-page":"360","DOI":"10.15330\/cmp.12.2.360-367","article-title":"Power Operations and Differentiations Associated With Supersymmetric Polynomials on a Banach Space","volume":"12","author":"Chernega","year":"2020","journal-title":"Carpathian Math. 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