Several remarks on norm attaining in tensor product spaces

2022/09/07 by Abraham Rueda Zoca, Zoca, Abraham Rueda
Mathematics · #FOS: Mathematics #Fixed Point Theorems Analysis #Functional Analysis (math.FA)

paper · pdf · doi:10.48550/arxiv.2209.02947

openalex publication_date 2022/09/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The aim of this note is to obtain results about when the norm of a projective tensor product is strongly subdifferentiable. We prove that if X⊗_πY is strongly subdifferentiable and either X or Y has the metric approximation property then every bounded operator from X to Y^* is compact. We also prove that (ℓ_p(I)⊗_πℓ_q(J))^* has the w^*-Kadec-Klee property for every non-empty sets I,J and every 2

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