Limited type subsets of locally convex spaces

2024/03/04 by Saak Gabriyelyan, Gabriyelyan, Saak
Computer Science · Mathematics · #46A3 #46E10 #Advanced Banach Space Theory #Advanced Topology and Set Theory #FOS: Mathematics #Functional Analysis (math.FA) #Optimization and Variational Analysis

paper · pdf · doi:10.48550/arxiv.2403.02016

openalex publication_date 2024/03/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let 1≤ p≤ q≤∞. Being motivated by the classical notions of limited, p-limited and coarse p-limited subsets of a Banach space, we introduce and study (p,q)-limited subsets and their equicontinuous versions and coarse p-limited subsets of an arbitrary locally convex space E. Operator characterizations of these classes are given. We compare these classes with the classes of bounded, (pre)compact, weakly (pre)compact and relatively weakly sequentially (pre)compact sets. If E is a Banach space, we show that the class of coarse 1-limited subsets of E coincides with the class of (1,∞)-limited sets, and if 1

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