Riesz type theorem in locally convex vector spaces

2012/12/06 by Miloslav Duchoň, Duchon, Miloslav
Computer Science · Mathematics · #Advanced Banach Space Theory #FOS: Mathematics #Fixed Point Theorems Analysis #Functional Analysis (math.FA) #Operator Algebras (math.OA) #Optimization and Variational Analysis

paper · pdf · doi:10.48550/arxiv.1212.1341

openalex publication_date 2012/12/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The present paper is concerned with some representatons of linear mappings of continuous functions into locally convex vector spaces, namely: If X is a complete Hausdorff locally convex vector space, then a general form of weakly compact mapping T:C[a,b]→ X is of the form Tg=∫_a^bg(t)dx(t), where the function x(⋅):[a,b] → X has a weakly compact semivariation on [a,b]. This theorem is a generalization of the result from Banach spaces to locally convex vector spaces.

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