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Nonfactorization in subsets of the measure algebra


Author: J. T. Burnham
Journal: Proc. Amer. Math. Soc. 35 (1972), 104-106
MSC: Primary 43A10; Secondary 42A96
DOI: https://doi.org/10.1090/S0002-9939-1972-0298342-9
MathSciNet review: 0298342
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Abstract: In this note we unify and simplify some recent results showing the impossibility of factoring in certain convolution subalgebras of the group algebra of a nondiscrete LCAG. A new result is a direct proof of nonfactorization of the classical Hardy spaces, regarded as convolution algebras, on the circle. By considering the ideal of Hilbert-Schmidt operators in the algebra of compact operators on a Hilbert space we illustrate that nonfactorization is not peculiar to convolution.


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DOI: https://doi.org/10.1090/S0002-9939-1972-0298342-9
Keywords: Convolution, measure algebras, factorization, Banach algebras, Segal algebras, normed ideals
Article copyright: © Copyright 1972 American Mathematical Society

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