Nonfactorization in subsets of the measure algebra

Burnham, J. T.

doi:10.1090/S0002-9939-1972-0298342-9

Nonfactorization in subsets of the measure algebra
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Proc. Amer. Math. Soc. 35 (1972), 104-106 Request permission

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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