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

Read, T. T.

doi:10.1090/S0002-9947-1971-0435853-0

The powers of a maximal ideal in a Banach algebra and analytic structure
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by T. T. Read

Trans. Amer. Math. Soc. 161 (1971), 235-248

DOI: https://doi.org/10.1090/S0002-9947-1971-0435853-0

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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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