Lack of isomorphic embeddings of ℓ_p,q into L_p,q(M,τ) over a noncommutative probability space

2024/04/10 by Jinghao Huang, Huang, Jinghao, Olga Sadovskaya +5
Mathematics · #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #Approximation Theory and Sequence Spaces #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.2404.06761

openalex publication_date 2024/04/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that the sequence space ℓ_p,q does not embed into L_p,q(M,τ) for any noncommutative probability space (M,τ), 1< p<∞ , 1≤ q<∞, p≠ q. Several applications to the isomorphic classification of noncommutative L_p,q-spaces are given, which extend and complement several earlier results.

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