BOUNDARIES FOR AN ALGEBRA OF BOUNDED HOLOMORPHIC FUNCTIONS

Title & Authors
BOUNDARIES FOR AN ALGEBRA OF BOUNDED HOLOMORPHIC FUNCTIONS

Abstract
Let $\small{A_b(B_E)}$ be the Banach algebra of all complex valued bounded continuous functions on the closed unit ball $\small{B_E}$ of a complex Banach space E, and holomorphic in the interior of $\small{B_E}$, endowed with the sup norm. We present some sufficient conditions for a set to be a boundary for $\small{A_b(B_E)}$ in case E belongs to a class of Banach spaces that includes the pre-dual of a Lorentz sequence space studied by Gowers in [6]. We also prove the non-existence of the Shilov boundary for $\small{A_b(B_E)}$ and give some examples of boundaries.
Keywords
Banach algebra;boundary;holomorphic functions;
Language
English
Cited by
1.
Boundaries for algebras of analytic functions on function module Banach spaces, Mathematische Nachrichten, 2014, 287, 7, 729
2.
Boundaries for algebras of holomorphic functions on Marcinkiewicz sequence spaces, Journal of Mathematical Analysis and Applications, 2006, 323, 2, 1116
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