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http://dx.doi.org/10.4134/JKMS.2004.41.1.231

BOUNDARIES FOR AN ALGEBRA OF BOUNDED HOLOMORPHIC FUNCTIONS  

Moraes, L.A. (Instituto de Matematica Universidade Federal do Rio de Janeiro)
Grados, L.-Romero (Universidade Estadual de Ponta Grossa)
Publication Information
Journal of the Korean Mathematical Society / v.41, no.1, 2004 , pp. 231-242 More about this Journal
Abstract
Let $A_b(B_E)$ be the Banach algebra of all complex valued bounded continuous functions on the closed unit ball $B_E$ of a complex Banach space E, and holomorphic in the interior of $B_E$, endowed with the sup norm. We present some sufficient conditions for a set to be a boundary for $A_b(B_E)$ 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 $A_b(B_E)$ and give some examples of boundaries.
Keywords
Banach algebra; boundary; holomorphic functions;
Citations & Related Records

Times Cited By Web Of Science : 3  (Related Records In Web of Science)
Times Cited By SCOPUS : 4
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