On injective tensor powers of ℓ₁

2020/12/24 by Ryan M. Causey, Elói Medina Galego, Causey, R. M. +3
Mathematics · #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #Advanced Operator Algebra Research #FOS: Mathematics #Functional Analysis (math.FA)

paper · pdf · doi:10.48550/arxiv.2012.13438

openalex publication_date 2020/12/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we prove that the 3-fold injective tensor product ℓ₁ \widehat⊗_ε ℓ₁ \widehat⊗_ε ℓ₁ is not isomorphic to any subspace of ℓ₁ \widehat⊗_ε ℓ₁. This result provides a new solution to a problem of Diestel on the projective tensor products of c₀. Moreover, this result implies that for any infinite countable compact space K, the 3-fold projective tensor product C(K) \widehat⊗_πC(K)\widehat⊗_πC(K) is not isomorphic to any quotient of C(K) \widehat⊗_πC(K).

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