The powers of a maximal ideal in a Banach algebra and analytic structure
Author:
T. T. Read
Journal:
Trans. Amer. Math. Soc. 161 (1971), 235248
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 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 .
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 P. C. Curtis, Jr., and A. FigáTalamanca, Factorization theorems for Banach algebras, Proc. Internat. Sympos. on Function Algebras (Tulane Univ., 1965), ScottForesman, Chicago, Ill., 1966, pp. 169185. MR 34 #3350. MR 0203500 (34:3350)
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 [4]
 A. M. Gleason, Finitely generated ideals in Banach algebras, J. Math. Mech. 13 (1964), 125132. MR 28 #2458. MR 0159241 (28:2458)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029947197104358530
PII:
S 00029947(1971)04358530
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
