A class of sets in a Banach space coarser than limited sets

A wide new class of subsets of a Banach space \(X\) named coarse \(p\)-limited sets (\( 1\leq p < \infty\)) is introduced by considering weak* \(p\)-summable sequences in \(X'\) instead of weak* null sequences. We study its basic properties and compare it with the class of compact and weakly...

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Bibliographic Details
Published inarXiv.org
Main Authors Galindo, Pablo, Miranda, V C C
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 10.08.2021
Subjects
Banach spaces
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Summary:A wide new class of subsets of a Banach space \(X\) named coarse \(p\)-limited sets (\( 1\leq p < \infty\)) is introduced by considering weak* \(p\)-summable sequences in \(X'\) instead of weak* null sequences. We study its basic properties and compare it with the class of compact and weakly compact sets. Results concerning the relationship of coarse \(p\)-limited sets with operators are obtained.
ISSN:2331-8422