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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

The powers of a maximal ideal in a Banach algebra and analytic structure


Author: T. T. Read
Journal: Trans. Amer. Math. Soc. 161 (1971), 235-248
MSC: Primary 46J20
MathSciNet review: 0435853
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Abstract: Sufficient conditions are given for the existence of an analytic variety at an element $ \phi $ of the spectrum of a commutative Banach algebra with identity. An associated graded algebra first considered by S. J. Sidney is used to determine the dimension of the analytic variety in terms of the closed powers of the maximal ideal which is the kernel of $ \phi $.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1971-0435853-0
PII: S 0002-9947(1971)0435853-0
Keywords: Cmmutative Banach algebra with identity, powers of a maximal ideal, analytic structure, dimension of an analytic variety, graded algebra
Article copyright: © Copyright 1971 American Mathematical Society