Frechet differentiability and quasi-polyhedrality in spaces of operators

2022/12/09 by Taduri Srinivasa Siva Rama Krishna Rao, Rao, Taduri Srinivasa Siva Rama Krishna
Mathematics · #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #Advanced Operator Algebra Research #math.FA

paper · pdf · doi:10.48550/arxiv.2212.05060

openalex publication_date 2022/12/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

Let X, Y be infinite dimensional, Banach spaces. Let L(X, Y) be the space of bounded operators . Motivated by the fact that smoothness of norm in the higher duals of even order of a Banach space can lead to Frechet differentiability, we exhibit classes of Banach spaces X, Y where very smooth points (i.e., smooth points that remain smooth in the bidual) in the space of compact operators K(X, Y) are Frechet smooth in L(X, Y) and hence in K(X, Y).

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