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arXiv · 1707.06847

A non-linear Bishop-Phelps-Bollob\'as type theorem

Sheldon Dantas·Domingo García·Sun Kwang Kim·Un Young Kim·Han Ju Lee·Manuel Maestre
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Abstract

The main aim of this paper is to prove a Bishop-Phelps-Bollob\'as type theorem on the unital uniform algebra A_{w^*u}(B_{X^*}) consisting of all w^*-uniformly continuous functions on the closed unit ball B_{X^*} which are holomorphic on the interior of B_{X^*}. We show that this result holds for A_{w^*u}(B_{X^*}) if X^* is uniformly convex or X^* is the uniformly complex convex dual space of an order continuous absolute normed space. The vector-valued case is also studied.

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Sheldon Dantas, Domingo García, Sun Kwang Kim, Un Young Kim, Han Ju Lee, Manuel Maestre. 2017-07-21. A non-linear Bishop-Phelps-Bollob\'as type theorem. https://arxiv.org/abs/1707.06847

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