A non-linear Bishop-Phelps-Bollobás type theorem

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

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

The main aim of this paper is to prove a Bishop-Phelps-Bollobás 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. Throughout the paper, we consider complex Banach spaces.

Original languageEnglish
Pages (from-to)7-16
Number of pages10
JournalQuarterly Journal of Mathematics
Volume70
Issue number1
DOIs
StatePublished - 1 Mar 2019

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