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arXiv · 1905.08483

Strong subdifferentiability and local Bishop-Phelps-Bollob\'as properties

Sheldon Dantas·Sun Kwang Kim·Han Ju Lee·Martin Mazzitelli
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Abstract

It has been recently presented some local versions of the Bishop-Phelps-Bollob\'as type property for operators. In the present article, we continue studying these properties for multilinear mappings. We show some differences between the local and uniform versions of the Bishop-Phelps-Bollob\'as type results for multilinear mappings, and also provide some interesting examples which shows that this study is not just a mere generalization of the linear case. We study those properties for bilinear forms on $\ell_p \times \ell_q$ using the strong subdifferentiability of the norm of the Banach space $\ell_p \hat{\otimes}_{\pi} \ell_{q}$. Moreover, we present necessary and sufficient conditions for the norm of a Banach space $Y$ to be strongly subdifferentiable through the study of these properties for bilinear mappings on $\ell_1^N \times Y$.

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Sheldon Dantas, Sun Kwang Kim, Han Ju Lee, Martin Mazzitelli. 2019-05-21. Strong subdifferentiability and local Bishop-Phelps-Bollob\'as properties. https://arxiv.org/abs/1905.08483

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