Birkhoff-James orthogonality in certain tensor products of Banach spaces II

2023/10/30 by Mohit, Ranjana Jain, Jain, Ranjana
Biochemistry, Genetics and Molecular Biology · Physics and Astronomy · #41A50 #46A32 #46B10 #46J50 #46M05 #Advanced Differential Geometry Research #Connective tissue disorders research #FOS: Mathematics #Fibroblast Growth Factor Research #Functional Analysis (math.FA)

paper · pdf · doi:10.48550/arxiv.2310.19442

openalex publication_date 2023/10/30 · openalex created_date 2023/11/01 · openalex updated_date 2026/08/01

Abstract

In this article, we discuss the relationship between Birkhoff-James orthogonality of elementary tensors in the space L^p(μ)⊗^Δ_pX, (1≤ p<∞) with the individual elements in their respective spaces, where X is a Banach space whose norm is Fr\acuteechet differentiable and Δ_p is the natural norm induced by L^p(μ,X). In order to study the said relationship, we first provide some characterizations of Birkhoff-James orthogonality of elements in the Lebesgue-Bochner space L^p(μ,X).

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