A non-linear Bishop-Phelps-Bollob\'as type theorem
Functional Analysis
2017-07-24 v1
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.
Cite
@article{arxiv.1707.06847,
title = {A non-linear Bishop-Phelps-Bollob\'as type theorem},
author = {Sheldon Dantas and Domingo García and Sun Kwang Kim and Un Young Kim and Han Ju Lee and Manuel Maestre},
journal= {arXiv preprint arXiv:1707.06847},
year = {2017}
}