{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,10]],"date-time":"2026-06-10T04:49:06Z","timestamp":1781066946062,"version":"3.54.1"},"reference-count":34,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2025,6,4]],"date-time":"2025-06-04T00:00:00Z","timestamp":1748995200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Natural Science Foundation of Inner Mongolia","award":["2023QN01012"],"award-info":[{"award-number":["2023QN01012"]}]},{"name":"Natural Science Foundation of Inner Mongolia","award":["2023MS01011"],"award-info":[{"award-number":["2023MS01011"]}]},{"name":"Inner Mongolia Autonomous Region Introduced High-level Talent Scientific Research Support Project","award":["2023QN01012"],"award-info":[{"award-number":["2023QN01012"]}]},{"name":"Inner Mongolia Autonomous Region Introduced High-level Talent Scientific Research Support Project","award":["2023MS01011"],"award-info":[{"award-number":["2023MS01011"]}]},{"name":"University Talent Research Start-up Fund of the Inner Mongolia University of Technology","award":["2023QN01012"],"award-info":[{"award-number":["2023QN01012"]}]},{"name":"University Talent Research Start-up Fund of the Inner Mongolia University of Technology","award":["2023MS01011"],"award-info":[{"award-number":["2023MS01011"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In this paper, we obtain some new upper bounds involving powers of the Davis\u2013Wielandt radius of bounded linear operators with closed ranges by using the Moore\u2013Penrose inverse. Moreover, by providing some examples, we show that the upper bounds obtained here are better than the existing ones in some situations.<\/jats:p>","DOI":"10.3390\/axioms14060439","type":"journal-article","created":{"date-parts":[[2025,6,4]],"date-time":"2025-06-04T06:00:49Z","timestamp":1749016849000},"page":"439","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["New Bounds for the Davis\u2013Wielandt Radius via the Moore\u2013Penrose Inverse of Bounded Linear Operators"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0009-0008-2417-4175","authenticated-orcid":false,"given":"Xiaomei","family":"Dong","sequence":"first","affiliation":[{"name":"College of Sciences, Inner Mongolia University of Technology, Hohhot 010051, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yuzhen","family":"Guo","sequence":"additional","affiliation":[{"name":"College of Sciences, Inner Mongolia University of Technology, Hohhot 010051, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3418-9051","authenticated-orcid":false,"given":"Deyu","family":"Wu","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2025,6,4]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Gustafson, K.E., and Rao, D.K.M. (1997). Numerical Range: The Field of Values of Linear Operators and Matrices, Springer.","DOI":"10.1007\/978-1-4613-8498-4_1"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Horn, R.A., and Johnson, C.R. (1991). Topics in Matrix Analysis, Cambridge University Press.","DOI":"10.1017\/CBO9780511840371"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"263","DOI":"10.1016\/0024-3795(82)90155-0","article-title":"On the numerical radius and its applications","volume":"42","author":"Goldberg","year":"1982","journal-title":"Linear Algebra Appl."},{"key":"ref_4","unstructured":"Groetsch, C.W. (1997). Generalized Inverses of Linear Operators: Representation and Approximation, Marcel Dekker."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"117","DOI":"10.1007\/s11785-024-01560-y","article-title":"Numerical radius and norm bounds via the Moore-Penrose inverse","volume":"18","author":"Sababheh","year":"2024","journal-title":"Complex Anal. Oper. Theory"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.laa.2025.02.013","article-title":"Improved numerical radius bounds using the Moore-Penrose inverse","volume":"711","author":"Bhunia","year":"2025","journal-title":"Linear Algebra Appl."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"659","DOI":"10.1080\/01630560500323083","article-title":"Weighted generalized inverses, oblique projections, and least-squares problems","volume":"26","author":"Corach","year":"2005","journal-title":"Numer. Funct. Anal. Optim."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.laa.2023.05.021","article-title":"Moore-Penrose inverse and partial orders on Hilbert space operators","volume":"674","author":"Fongi","year":"2023","journal-title":"Linear Algebra Appl."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1007\/BF01212904","article-title":"Das algebraische Analogon zu einem Satze von Fej\u00e9r","volume":"2","author":"Toeplitz","year":"1918","journal-title":"Math. Z."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"323","DOI":"10.1016\/j.laa.2019.01.019","article-title":"A generalization of the numerical radius","volume":"569","author":"Kittaneh","year":"2019","journal-title":"Linear Algebra Appl."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1995","DOI":"10.1080\/03081087.2020.1781037","article-title":"Some improvements of numerical radius inequalities of operators and operator matrices","volume":"70","author":"Bhunia","year":"2022","journal-title":"Linear Multilinear Algebra"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"397","DOI":"10.1007\/s11117-018-0613-2","article-title":"Characterization of numerical radius parallelism in C*-algebras","volume":"23","author":"Zamani","year":"2019","journal-title":"Positivity"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"114","DOI":"10.1016\/j.laa.2020.08.032","article-title":"Another generalization of the numerical radius for Hilbert space operators","volume":"609","author":"Zamani","year":"2021","journal-title":"Linear Algebra Appl."},{"key":"ref_14","first-page":"980","article-title":"Some A-numerical radius inequalities for semi-Hilbertian space operators","volume":"69","author":"Sahoo","year":"2020","journal-title":"Linear Multilinear Algebra"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Liu, J., Wu, D., and Chen, A. (2025). The upper bounds of the numerical radius on Hilbert C*-modules. Axioms, 14.","DOI":"10.3390\/axioms14030199"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"681","DOI":"10.1007\/s40574-021-00307-3","article-title":"Some generalizations of A-numerical radius inequalities for semi-Hilbert space operators","volume":"14","author":"Guesba","year":"2021","journal-title":"Boll. Unione Mat. Ital."},{"key":"ref_17","first-page":"69","article-title":"The shell of a Hilbert space operator","volume":"29","author":"Davis","year":"1968","journal-title":"Acta Sci. Math."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"633","DOI":"10.2140\/pjm.1955.5.633","article-title":"On eigenvalues of sums of normal matrices","volume":"5","author":"Wielandt","year":"1955","journal-title":"Pacific J. Math."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"2147","DOI":"10.1080\/03081087.2018.1484422","article-title":"Norm-parallelism and the Davis-Wielandt radius of Hilbert space operators","volume":"67","author":"Zamani","year":"2019","journal-title":"Linear Multilinear Algebra"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1158","DOI":"10.1080\/03081087.2022.2056116","article-title":"Davis-Wielandt radius inequalities for off-diagonal operator matrices","volume":"71","author":"Dong","year":"2023","journal-title":"Linear Multilinear Algebra"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"767","DOI":"10.7153\/oam-2023-17-50","article-title":"Further refinements of Davis-Wielandt radius inequalities","volume":"17","author":"Bhunia","year":"2023","journal-title":"Oper. Matrices"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s00009-019-1458-z","article-title":"Some upper bounds for the Davis-Wielandt radius of Hilbert space operators","volume":"17","author":"Zamani","year":"2020","journal-title":"Mediterr. J. Math."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s43034-020-00102-9","article-title":"Bounds for the Davis-Wielandt radius of bounded linear operators","volume":"12","author":"Bhunia","year":"2021","journal-title":"Ann. Funct. Anal."},{"key":"ref_24","first-page":"1","article-title":"New inequalities for Davis\u2013Wielandt radius of Hilbert space operators","volume":"2","author":"Bhunia","year":"2021","journal-title":"Bull. Malays. Math. Sci. Soc."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1804","DOI":"10.1080\/03081087.2022.2081308","article-title":"On the Davis-Wielandt radius inequalities of Hilbert space operators","volume":"71","author":"Alomari","year":"2023","journal-title":"Linear Multilinear Algebra"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s40590-024-00631-6","article-title":"A generalization of the Davis-Wielandt radius for operators","volume":"30","author":"Alomari","year":"2024","journal-title":"Bol. Soc. Mat. Mex."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"283","DOI":"10.1007\/s00009-022-02195-z","article-title":"Some sharp estimations for Davis-Wielandt radius in B(H)","volume":"19","author":"Moghaddam","year":"2022","journal-title":"Mediterr. J. Math."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s41980-024-00926-4","article-title":"A-Davis-Wielandt radius bounds of semi-Hilbertian space operators","volume":"50","author":"Guesba","year":"2024","journal-title":"Bull. Iran. Math. Soc."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"283","DOI":"10.2977\/prims\/1195175202","article-title":"Notes on some inequalities for Hilbert space operators","volume":"24","author":"Kittaneh","year":"1988","journal-title":"Publ. Res. Inst. Math. Sci."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"827","DOI":"10.2298\/FIL1204827K","article-title":"A commutator approach to Buzano\u2019s inequality","volume":"26","author":"Khosravi","year":"2012","journal-title":"Filomat"},{"key":"ref_31","first-page":"405","article-title":"Generalizzazione della diseguaglianza di Cauchy-Schwarz","volume":"31","author":"Buzano","year":"1974","journal-title":"Rend. Sem. Mat. Univ. Politech. Torino."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"341","DOI":"10.2989\/16073606.2023.2226911","article-title":"Upper bounds for the numerical radii of powers of Hilbert space operators","volume":"47","author":"Aldolat","year":"2024","journal-title":"Quaest. Math."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"341","DOI":"10.7153\/oam-02-20","article-title":"Davis-Wielandt shells of operators","volume":"2","author":"Li","year":"2008","journal-title":"Oper. Matrices"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"133","DOI":"10.4064\/sm182-2-3","article-title":"Numerical radius inequalities for Hilbert space operators. II","volume":"182","author":"Kittaneh","year":"2007","journal-title":"Stud. Math."}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/14\/6\/439\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T17:46:23Z","timestamp":1760031983000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/14\/6\/439"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,6,4]]},"references-count":34,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2025,6]]}},"alternative-id":["axioms14060439"],"URL":"https:\/\/doi.org\/10.3390\/axioms14060439","relation":{},"ISSN":["2075-1680"],"issn-type":[{"value":"2075-1680","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,6,4]]}}}