STANDARD IDEALS IN WEIGHTED ALGEBRAS OF KORENBLYUM AND WIENER TYPES

We introduce two types of Banach algebras of analytic functions on the unit disc which can be seen as weighted versions of closed primary ideals of the Korenblyum and (analytic) Wiener algebras, respectively. Such types of algebras arise in connection with convolution Banach algebras of Sobolev type...

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Bibliographic Details
Published in:Mathematica scandinavica 2011-01, Vol.108 (2), p.291-319
Main Authors: GALÉ, JOSÉ E., WAWRZYŃCZYK, ANTONI
Format: Article
Language:English
Subjects:
Abstract algebra
Algebra
Analytic functions
Banach space
Fourier series
Integers
Mathematical theorems
Subalgebras
Taylor series
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Summary:We introduce two types of Banach algebras of analytic functions on the unit disc which can be seen as weighted versions of closed primary ideals of the Korenblyum and (analytic) Wiener algebras, respectively. Such types of algebras arise in connection with convolution Banach algebras of Sobolev type, on the positive half-line, and their discrete analogues defined in terms of higher order differences. We show that all closed ideals are standard for algebras in the first class, and that closed ideals with countable hull are standard in algebras of the second class.
ISSN:0025-5521
1903-1807
DOI:10.7146/math.scand.a-15173