On collectively L-weakly compact sets of operators

2024/07/15 by Eduard Emelyanov, Emelyanov, Eduard
Decision Sciences · Mathematics · #46B50 #47B01 #47B07 #47B65 #Advanced Banach Space Theory #Approximation Theory and Sequence Spaces #FOS: Mathematics #Functional Analysis (math.FA) #Fuzzy and Soft Set Theory

paper · pdf · doi:10.48550/arxiv.2407.10455

openalex publication_date 2024/07/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A set of bounded linear operators from a Banach space to a Banach lattice is collectively L-weakly compact whenever union of images of the unit ball is L-weakly compact. We extend the Meyer-Nieberg duality theorem to collectively L-weakly compact sets of operators, study relations between these sets and collectively almost limited sets, and discuss the domination problem for collectively compact sets and collectively L-weakly compact sets.

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