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arXiv · 1604.01461

The strong Bishop-Phelps-Bollob\'as property

Sheldon Dantas
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Abstract

In this paper we introduce the strong Bishop-Phelps-Bollob\'as property (sBPBp) for bounded linear operators between two Banach spaces $X$ and $Y$. This property is motivated by a Kim-Lee result which states, under our notation, that a Banach space $X$ is uniformly convex if and only if the pair $(X,\mathbb{K})$ satisfies the sBPBp. Positive results of pairs of Banach spaces $(X,Y)$ satisfying this property are given and concrete pairs of Banach spaces $(X, Y)$ failing it are exhibited. A complete characterization of the sBPBp for the pairs $(\ell_p, \ell_q)$ is also provided.

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Sheldon Dantas. 2016-04-06. The strong Bishop-Phelps-Bollob\'as property. https://arxiv.org/abs/1604.01461

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