Banach algebras, logarithms, and polynomials of convolution type

Abstract

Using elementary Banach algebra techniques, it is determined which elements of Banach algebras like l 1( 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.