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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Subharmonic functions and uniform algebras


Author: Donna Kumagai
Journal: Proc. Amer. Math. Soc. 78 (1980), 23-29
MSC: Primary 46J10; Secondary 31C05, 32E25
DOI: https://doi.org/10.1090/S0002-9939-1980-0548077-4
MathSciNet review: 548077
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Abstract: Recently Aupetit and Wermer [J. Functional Anal. 28 (1978), 386-400] have shown conditions under which analytic structure exists in the spectrum space of a uniform algebra. Their work makes critical use of subharmonicity properties of certain classes of functions. In this paper, we develop a technique which offers an alternate and unified proof for subharmonicity of the functions in their paper assuming Basener's generalized Shilov boundary conjecture. Our technique uses the Oka-Wermer method applied to the n-fold tensor product of the algebra. We exhibit further applications of our main result including a special case which holds for all uniform algebras.


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DOI: https://doi.org/10.1090/S0002-9939-1980-0548077-4
Keywords: Subharmonicity, maximal ideal space, generalized Shilov boundary
Article copyright: © Copyright 1980 American Mathematical Society

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