Banach algebras, logarithms, and polynomials of convolution type
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AbstractUsing elementary Banach algebra techniques, it is determined which elements of Banach algebras like l1(α), b(K), and A have logarithms. The Wiener-Lévy theorem will be used to answer the same question for more complicated Banach algebras like the Wiener algebra. These results will be applied to polynomials of convolution type and a generalization thereof.

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