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arXiv · 2212.05060

Frechet differentiability and quasi-polyhedrality in spaces of operators

Taduri Srinivasa Siva Rama Krishna Rao
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Abstract

Let $X, Y$ be infinite dimensional, Banach spaces. Let $\mathcal{L}(X, Y)$ 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 $\mathcal{K}(X, Y)$ are Frechet smooth in $\mathcal{L}(X, Y)$ and hence in $\mathcal{K}(X, Y)$.

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Taduri Srinivasa Siva Rama Krishna Rao. 2022-12-09. Frechet differentiability and quasi-polyhedrality in spaces of operators. https://arxiv.org/abs/2212.05060

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