Boundaries for algebras of holomorphic functions on Marcinkiewicz sequence spaces |
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Authors: | Yun Sung Choi |
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Institution: | Department of Mathematics, Pohang University of Science and Technology, Pohang, 790-784, Republic of Korea |
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Abstract: | Let Ab(E) be the Banach algebra of all complex-valued bounded continuous functions on the closed unit ball BE of a complex Banach space E and holomorphic in the interior of BE and let Au(E) be the closed subalgebra of those functions which are uniformly continuous on BE. For the case whose bidual is a Marcinkiewicz sequence space Mw, we describe some sufficient conditions for a set to be a boundary of either Ab(E) or Au(E). Moreover, we consider some analogous problems on to those which were studied on the Gowers space Gp of characteristic p by Grados and Moraes L.R. Grados, L.A. Moraes, Boundaries for algebras of holomorphic functions, J. Math. Anal. Appl. 281 (2003) 575-586; L.R. Grados, L.A. Moraes, Boundaries for an algebra of bounded holomorphic functions, J. Korean Math. Soc. 41 (1) (2004) 231-242]. |
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Keywords: | Holomorphic function Shilov boundary Marcinkiewicz sequence space J Globevnik L R Grados L A Moraes |
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