On characterization of locally L⁰-convex topologies induced by a family of L⁰-seminorms

2014/04/01 by José Miguel Zapata, García, José Miguel Zapata · 1 citation
Computer Science · Mathematics · #Advanced Banach Space Theory #FOS: Mathematics #Functional Analysis (math.FA) #Numerical methods in inverse problems #Optimization and Variational Analysis

paper · pdf · doi:10.48550/arxiv.1404.0357

openalex publication_date 2014/04/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

The purpose of this paper is to provide a characterization of the topological L⁰-modules whose topology is induced by a family of L⁰-seminorms using the gauge function for L⁰-modules. Taking advantage of these ideas we will give a counterexample of a locally L⁰-convex module whose topology is not induced by a family of L⁰-seminorms.

Cited by

• Random convex analysis (I): separation and Fenchel-Moreau duality in random locally convex modules

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