A Banach space characterization of (sequentially) Ascoli spaces

2023/07/21 by Saak Gabriyelyan, Gabriyelyan, Saak
Mathematics · #46A3 #54C10 #54D99 #Advanced Banach Space Theory #Advanced Topics in Algebra #Advanced Topology and Set Theory #FOS: Mathematics #Functional Analysis (math.FA) #General Topology (math.GN)

paper · pdf · doi:10.48550/arxiv.2307.11561

openalex publication_date 2023/07/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that a Tychonoff space X is an Ascoli space (resp., a sequentially Ascoli space) if and only if for each Banach space E, every k-continuous and almost k-compact (resp., almost k-sequential) map T form X into the Banach dual E' of E is continuous.

Related

• Ascoli and sequentially Ascoli spaces
• Functions on products X × Y with applications to Ascoli spaces, k_ℝ-spaces and s_ℝ-spaces
• Ascoli's theorem for pseudocompact spaces
• The Ascoli property for function spaces and the weak topology of Banach and Fréchet spaces
• Asplund spaces C_k(X) beyond Banach spaces