Some remarks on the weak maximizing property
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comunitat-uji-handle2:10234/7037
comunitat-uji-handle3:10234/8635
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INVESTIGACIONMetadatos
Título
Some remarks on the weak maximizing propertyFecha de publicación
2021-06-16Editor
Elsevier; Academic PressISSN
0022-247XCita bibliográfica
DANTAS, Sheldon; JUNG, Mingu; MARTÍNEZ-CERVANTES, Gonzalo. Some remarks on the weak maximizing property. Journal of Mathematical Analysis and Applications, 2021, p. 125433.Tipo de documento
info:eu-repo/semantics/articleVersión de la editorial
http://www.journals.elsevier.com/journal-of-mathematical-analysis-and-applications/Versión
info:eu-repo/semantics/acceptedVersionPalabras clave / Materias
Resumen
A pair of Banach spaces is said to have the weak maximizing property (WMP, for short) if for every bounded linear operator T from E into F, the existence of a non-weakly null maximizing sequence for T implies that T ... [+]
A pair of Banach spaces is said to have the weak maximizing property (WMP, for short) if for every bounded linear operator T from E into F, the existence of a non-weakly null maximizing sequence for T implies that T attains its norm. This property was recently introduced in a paper by R. Aron, D. García, D. Pelegrino and E. Teixeira, raising several open questions. The aim of the present paper is to contribute to the better knowledge of the WMP and its limitations. Namely, we provide sufficient conditions for a pair of Banach spaces to fail the WMP and study the behavior of this property with respect to quotients, subspaces, and direct sums, which open the gate to present several consequences. For instance, we deal with pairs of the form , proving that these pairs fail the WMP whenever or . We also show that, under certain conditions on E, the assumption that has the WMP for every Banach space F implies that E must be finite dimensional. On the other hand, we show that has the WMP for every reflexive space E if and only if F has the Schur property. We also give a complete characterization for the pairs to have the WMP by calculating the moduli of asymptotic uniform convexity of and of asymptotic uniform smoothness of when . We conclude the paper by discussing some variants of the WMP and presenting a list of open problems on the topic of the paper. [-]
Publicado en
J. Math. Anal. Appl. 504 (2021) 125433Entidad financiadora
Fundación Séneca | Agencia Estatal de Investigación | European Social Fund (ESF) | Youth European Initiative (YEI) | Estonian Research Council | Spanish AEI
Código del proyecto o subvención
PID2019 - 106529GB - I00 / AEI / 10.13039/501100011033 | PGC2018 - 093794 - B - I00 | CZ.02.1.01/0.0/0.0/16_019/0000778 | PRG877 | NRF-2019R1A2C1003857 | 20797/PI/18 | MTM2017-86182-P | 21319/PDGI/19
Derechos de acceso
© 2021 Elsevier Inc. All rights reserved.
info:eu-repo/semantics/openAccess
info:eu-repo/semantics/openAccess
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