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 ≤ p < ∞ ) 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 conce...

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Bibliographic Details
Published inBoletim da Sociedade Brasileira de Matemática Vol. 53; no. 3; pp. 941 - 955
Main Authors Galindo, Pablo, Miranda, V. C. C.
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 2022
Springer Nature B.V
Subjects
Banach spaces
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Theoretical
summable sequences
coarse
limited sets
46B20
Gelfand–Phillips property
Dunford–Pettis property
weak
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Summary:A wide new class of subsets of a Banach space X named coarse p -limited sets ( 1 ≤ p < ∞ ) 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:1678-7544
1678-7714
DOI:10.1007/s00574-022-00290-z