Barreled extended locally convex spaces and Uniform boundedness principle

2023/05/23 by Akshay Kumar, Kumar, Akshay, Varun Jindal +1
Decision Sciences · Mathematics · #46A03 #46A08 #46A17 #46A20 #54C40 #Advanced Banach Space Theory #Advanced Topology and Set Theory #FOS: Mathematics #Functional Analysis (math.FA) #Fuzzy and Soft Set Theory

paper · pdf · doi:10.48550/arxiv.2305.13816

openalex publication_date 2023/05/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For an extended locally convex space (X,τ), in [8], the authors studied the finest locally convex topology (flc topology) τ_F on X coarser than τ. One can often prove facts about (X, τ) by applying classical locally convex space theory on (X, τ_F). This paper employs the flc topology to analyze barreled extended locally convex spaces and establish the uniform boundedness principle in the extended setting. One of the key results of this paper is the relationship between the barreledness of an extended locally convex space (X,τ) and the barreledness of the associated finest locally convex space (X, τ_F). This is achieved by examining the lower semi-continuous seminorms on these spaces.

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