Article ID Journal Published Year Pages File Type
4616361 Journal of Mathematical Analysis and Applications 2014 11 Pages PDF
Abstract
In this paper we study some geometrical properties of certain classes of uniform algebras, in particular the ball algebra Au(BX) of all uniformly continuous functions on the closed unit ball and holomorphic on the open unit ball of a complex Banach space X. We prove that Au(BX) has k-numerical index 1 for every k, the lushness and also the AHSP. Moreover, the disk algebra A(D), and more in general any uniform algebra whose Choquet boundary has no isolated points, is proved to have the polynomial Daugavet property. Most of those properties are extended to the vector valued version AX of a uniform algebra A.
Related Topics
Physical Sciences and Engineering Mathematics Analysis
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