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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