{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:33:23Z","timestamp":1760060003084,"version":"build-2065373602"},"reference-count":36,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2025,7,23]],"date-time":"2025-07-23T00:00:00Z","timestamp":1753228800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>Suppose X and Y are Banach spaces, K is a compact Hausdorff space, and C(K,\u00a0X) is the Banach space of all continuous X-valued functions (with the supremum norm). We will study some strongly bounded operators T:C(K,\u00a0X)\u2192Y with representing measures m:\u03a3\u2192L(X,Y), where L(X,Y) is the Banach space of all operators T:X\u2192Y and \u03a3 is the \u03c3-algebra of Borel subsets of K. The classes of operators that we will discuss are the Grothendieck, p-limited, p-compact, limited, operators with completely continuous, unconditionally converging, and p-converging adjoints, compact, and absolutely summing. We give a characterization of the limited operators (resp. operators with completely continuous, unconditionally converging, p-convergent adjoints) in terms of their representing measures.<\/jats:p>","DOI":"10.3390\/axioms14080558","type":"journal-article","created":{"date-parts":[[2025,7,23]],"date-time":"2025-07-23T14:22:44Z","timestamp":1753280564000},"page":"558","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["On the Characterizations of Some Strongly Bounded Operators on C(K, X) Spaces"],"prefix":"10.3390","volume":"14","author":[{"given":"Ioana","family":"Ghenciu","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Wisconsin-River Falls, River Falls, WI 54022, USA"}]}],"member":"1968","published-online":{"date-parts":[[2025,7,23]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"139","DOI":"10.1090\/S0002-9947-1974-0338821-5","article-title":"Linear Operators and Vector Measures","volume":"192","author":"Brooks","year":"1974","journal-title":"Trans. Am. Math. Soc."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Diestel, J., and Uhl, J.J. (1977). Vector Measures, American Mathematical Society. Mathematical Surveys and Monographs Volume 15.","DOI":"10.1090\/surv\/015"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"215","DOI":"10.1016\/0022-1236(69)90012-3","article-title":"Linear bounded transformations on the space of continuous functions","volume":"4","author":"Batt","year":"1969","journal-title":"J. Funct. Anal."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Dinculeanu, N. (1967). Vector Measures, Pergamon Press.","DOI":"10.1016\/B978-1-4831-9762-3.50004-4"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"13","DOI":"10.21136\/CMJ.1971.101000","article-title":"On representation of linear operators on C0(T, X)","volume":"21","author":"Dobrakov","year":"1971","journal-title":"Czechoslovak. Math. J."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"2569","DOI":"10.1007\/s40995-019-00743-z","article-title":"A study on Dunford-Pettis completely continuous like operators","volume":"43","author":"Alikhani","year":"2019","journal-title":"Iran. J. Sci. Technol. Trans. A Sci."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"137","DOI":"10.1017\/S0305004100062678","article-title":"Characterizations of some classes of operators on spaces of vector-valued continuous functions","volume":"97","author":"Bombal","year":"1985","journal-title":"Math. Proc. Camb. Phil. Soc."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"355","DOI":"10.1002\/mana.19891430125","article-title":"Strictly singular and strictly cosingular operators on C(K, E)","volume":"143","author":"Bombal","year":"1989","journal-title":"Math. Nachr."},{"key":"ref_9","first-page":"43","article-title":"Dunford-Pettis like properties of continuous vector function spaces","volume":"6","author":"Castillo","year":"1993","journal-title":"Rev. Mat. Univ. Complut. Madrid"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"21","DOI":"10.2989\/16073606.2023.2182243","article-title":"A note on some classes of operators on C(K, X)","volume":"47","author":"Ghenciu","year":"2023","journal-title":"Quaest. Math."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"63","DOI":"10.1007\/s10474-018-0893-9","article-title":"An isomorphic property in spaces of compact operators and some classes of operators on C(K, X)","volume":"157","author":"Ghenciu","year":"2019","journal-title":"Acta Math. Hungar."},{"key":"ref_12","first-page":"261","article-title":"On some classes of operators on C(K, X)","volume":"63","author":"Ghenciu","year":"2015","journal-title":"Bull. Polish. Acad. Sci. Math."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1007\/BF01202500","article-title":"Some classes of operators on C(K, E). Extensions and applications","volume":"47","author":"Bombal","year":"1986","journal-title":"Arch. Math."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"2285","DOI":"10.1090\/S0002-9939-97-03763-5","article-title":"Grothendieck operators on tensor products","volume":"125","author":"Domanski","year":"1997","journal-title":"Proc. Am. Math. Soc."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"177","DOI":"10.1002\/mana.19901490114","article-title":"A Gelfand-Phillips property with respect to the weak topology","volume":"149","author":"Leung","year":"1990","journal-title":"Math. Nachr."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1002\/mana.19841190105","article-title":"Limited operators and strict cosingularity","volume":"119","author":"Bourgain","year":"1984","journal-title":"Math. Nachr."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Diestel, J., Jarchow, H., and Tonge, A. (1995). Absolutely Summing Operators, Cambridge University Press. Cambridge Stud. Adv. Math, 43.","DOI":"10.1017\/CBO9780511526138"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Ryan, R.A. (2002). Introduction to Tensor Products of Banach Spaces, Springer.","DOI":"10.1007\/978-1-4471-3903-4"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"563","DOI":"10.2989\/16073606.2017.1301591","article-title":"On weak-star-p-convergent operators","volume":"40","author":"Fourie","year":"2017","journal-title":"Quaest. Math."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"420","DOI":"10.1002\/mana.201600335","article-title":"Pe\u0142czy\u0144ski\u2019s Property (V*) of order p and its quantification","volume":"291","author":"Li","year":"2018","journal-title":"Math. Nach."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Ghenciu, I. (2018). The p-Gelfand Phillips Property in Spaces of Operators and Dunford-Pettis like sets. Acta Math. Hungar., 1\u201319.","DOI":"10.1007\/s10474-018-0836-5"},{"key":"ref_22","first-page":"427","article-title":"An operator summability of sequences in Banach spaces","volume":"56","author":"Karn","year":"2014","journal-title":"Math. J."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"17","DOI":"10.4064\/sm150-1-3","article-title":"Compact operators whose adjoints factor through subspaces of \u2113p","volume":"150","author":"Sinha","year":"2002","journal-title":"Studia Math."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Diestel, J. (1984). Sequences and Series in Banach Spaces, Springer. Grad. Texts in Math., no. 92.","DOI":"10.1007\/978-1-4612-5200-9"},{"key":"ref_25","unstructured":"Semadeni, Z. (1971). Banach Spaces of Continuous Functions, PWN."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"211","DOI":"10.4064\/sm-18-2-211-222","article-title":"Spaces of continuous functions (III)","volume":"18","author":"Semadeni","year":"1959","journal-title":"Studia Math."},{"key":"ref_27","first-page":"237","article-title":"Some mapping properties of representing measures","volume":"iV","author":"Bilyeu","year":"1976","journal-title":"Annali Mat. Pura Appl."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"123","DOI":"10.1090\/S0002-9947-1973-0320796-5","article-title":"Absolutely summing and dominated operators on spaces of vector-valued continuous functions","volume":"179","author":"Swartz","year":"1973","journal-title":"Trans. Am. Math. Soc."},{"key":"ref_29","first-page":"35","article-title":"The weak Gelfand-Phillips property in spaces of compact operators","volume":"58","author":"Ghenciu","year":"2017","journal-title":"Comment. Math. Univ. Carolin."},{"key":"ref_30","first-page":"713","article-title":"A note on p-limited sets","volume":"410","author":"Delgado","year":"2014","journal-title":"J. Math. Appl."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"291","DOI":"10.4064\/sm197-3-6","article-title":"Operators whose adjoints are quasi p-nuclear","volume":"197","author":"Delgado","year":"2010","journal-title":"Studia Math."},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Ghenciu, I. A note on p-limited sets in dual Banach spaces. Monatsh. Math., 2022.","DOI":"10.1007\/s00605-022-01738-6"},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Lacey, H.E. (1974). The Isometric Theory of Classical Banach Spaces, Springer.","DOI":"10.1007\/978-3-642-65762-7"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"362","DOI":"10.2307\/2373824","article-title":"Pointwise compact subsets of the first Baire class","volume":"99","author":"Rosenthal","year":"1977","journal-title":"Am. J. Math."},{"key":"ref_35","first-page":"155","article-title":"A dual characterization of Banach spaces not containing \u21131","volume":"34","author":"Emmanuele","year":"1986","journal-title":"Bull. Acad. Sci. Math."},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Cembranos, P., and Mendoza, J. (1997). Banach Spaces of Vector-Valued Functions, Springer. Lecture Notes in Math., 1676.","DOI":"10.1007\/BFb0096765"}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/14\/8\/558\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T18:14:50Z","timestamp":1760033690000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/14\/8\/558"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,7,23]]},"references-count":36,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2025,8]]}},"alternative-id":["axioms14080558"],"URL":"https:\/\/doi.org\/10.3390\/axioms14080558","relation":{},"ISSN":["2075-1680"],"issn-type":[{"type":"electronic","value":"2075-1680"}],"subject":[],"published":{"date-parts":[[2025,7,23]]}}}