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Proceedings of the American Mathematical Society

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

 

 

Algebraic structure in complex function spaces


Author: A. J. Ellis
Journal: Proc. Amer. Math. Soc. 107 (1989), 621-626
MSC: Primary 46J10; Secondary 46E25
DOI: https://doi.org/10.1090/S0002-9939-1989-0975640-7
MathSciNet review: 975640
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Abstract: Let $ M$ be a complex function space containing constants, and let $ Z$ be the complex state space of $ M$. If $ M$ is linearly isometric to a uniform algebra and if $ Z$ is affinely homeomorphic to the complex state space of a uniform algebra then we prove that $ M$ is a uniform algebra. Neither of the two conditions taken separately imply this conclusion.


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DOI: https://doi.org/10.1090/S0002-9939-1989-0975640-7
Keywords: Complex state space, linear isometry
Article copyright: © Copyright 1989 American Mathematical Society