A class of sets in a Banach space coarser than limited sets
Pablo Galindo, V. C. C. Miranda

TL;DR
This paper introduces coarse p-limited sets in Banach spaces, a new class based on weak* p-summable sequences, and explores their properties and relationships with compact sets and operators.
Contribution
It defines and analyzes coarse p-limited sets, a novel class in Banach space theory, expanding understanding of set classifications and operator interactions.
Findings
Coarse p-limited sets are distinct from compact and weakly compact sets.
The paper establishes relationships between coarse p-limited sets and bounded linear operators.
Properties of coarse p-limited sets are characterized in various Banach space contexts.
Abstract
A wide new class of subsets of a Banach space named coarse -limited sets () is introduced by considering weak* -summable sequences in 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 -limited sets with operators are obtained.
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Taxonomy
TopicsAdvanced Banach Space Theory · Approximation Theory and Sequence Spaces · Advanced Harmonic Analysis Research
