Isomorphic classification of projective tensor products of spaces of continuous functions

2022/01/20 by Ryan M. Causey, Elói Medina Galego, Causey, R. M. +2
Mathematics · #Advanced Banach Space Theory #Advanced Topology and Set Theory #FOS: Mathematics #Functional Analysis (math.FA) #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2201.08271

openalex publication_date 2022/01/20 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28

Abstract

We prove that for infinite, countable, compact, Hausdorff spaces K,L, C(K)\widehat⊗_πC(L) is isomorphic to exactly one of the spaces C(ω^ωξ)\widehat⊗_πC(ω^ωζ), 0\leqslant ζ\leqslant ξ<ω₁. We also prove that C(K)\widehat⊗_πC(L) is not isomorphic to C(M) for any compact, Hausdorff space M.

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