On the Random Conjugate Spaces of a Random Locally Convex Module

2011/03/16 by Tiexin Guo, Guo Tiexin, Tiexin, Guo +3
Computer Science · Decision Sciences · Mathematics · #46A05 #46A16 #46A20 #46A22 #46A25 #Advanced Banach Space Theory #FOS: Mathematics #Functional Analysis (math.FA) #Optimization and Variational Analysis #Risk and Portfolio Optimization #math.FA #msc:46A05 #msc:46A16 #msc:46A20 #msc:46A22 #msc:46A25

paper · pdf · doi:10.48550/arxiv.1103.3127

10 pages

arxiv created 2011/03/16 · openalex publication_date 2011/03/16 · arxiv updated 2011/03/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Theoretically speaking, there are four kinds of possibilities to define the random conjugate space of a random locally convex module. The purpose of this paper is to prove that among the four kinds there are only two which are universally suitable for the current development of the theory of random conjugate spaces: in this process we also obtain a somewhat surprising and crucial result that for a random normed module with base (Ω,\cal F,P) such that (Ω,\cal F,P) is nonatomic then the random normed module is a totally disconnected topological space when it is endowed with the locally L⁰-convex topology.

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