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arXiv · 2108.04793

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

Pablo Galindo·V. C. C. Miranda
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Abstract

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.

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Pablo Galindo, V. C. C. Miranda. 2021-08-10. A class of sets in a Banach space coarser than limited sets. https://arxiv.org/abs/2108.04793

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