On isomorphisms of Banach spaces of continuous functions

2013/02/13 by Grzegorz Plebanek, Plebanek, Grzegorz
Mathematics · #46B03 #46E15 #Advanced Banach Space Theory #Advanced Topology and Set Theory #Approximation Theory and Sequence Spaces #FOS: Mathematics #Functional Analysis (math.FA) #Primary 46B26

paper · pdf · doi:10.48550/arxiv.1302.3211

openalex publication_date 2013/02/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that if K and L are compact spaces and C(K) and C(L) are isomorphic as Banach spaces then K has a π-base consisting of open sets U such that U is a continuous image of some compact subspace of L. This gives some information on isomorphic classes of the spaces of the form C([0,1]^κ) and C(K) where K is Corson compact.

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