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 language | English |
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Pages (from-to) | 7-16 |
Number of pages | 10 |
Journal | Quarterly Journal of Mathematics |
Volume | 70 |
Issue number | 1 |
DOIs | |
State | Published - 1 Mar 2019 |