Quantitative Schur Property and Measures of Weak Non-Compactness

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F25%3A10509885" target="_blank" >RIV/00216208:11320/25:10509885 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=zdFBcg.8Tg" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=zdFBcg.8Tg</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00025-025-02550-y" target="_blank" >10.1007/s00025-025-02550-y</a>

Result language
angličtina
Original language name
Quantitative Schur Property and Measures of Weak Non-Compactness
Original language description
We compare several versions of the quantitative Schur property of Banach spaces. We establish their equivalence up to multiplicative constants and provide examples clarifying when the change of constants is necessary. We also give exact results on preservation of the quantitative Schur property by finite or infinite direct sums. We further prove a sufficient condition for the 1-Schur property which simplifies and generalizes previous results. We study in more detail relationship of the quantitative Schur property to quantitative weak sequential completeness and to equivalence of measures of weak non-compactness. We also illustrate the difference of real and complex settings. To this end we prove and use the optimal version of complex quantiative Rosenthal & ell;1documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$ell _1$$end{document}-theorem. Finally, we give two examples of Lipschitz-free spaces over countable graphs which have quantitative Schur property, but not the 1-Schur property.
Czech name
—
Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GA23-04776S" target="_blank" >GA23-04776S: Interplay of algebraic, metric, geometric and topological structures on Banach spaces</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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