Banach algebras with uncomplemented radical

Bachelis, Gregory F.; Saeki, Sadahiro

doi:10.1090/S0002-9939-1987-0884465-0

Banach algebras with uncomplemented radical
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by Gregory F. Bachelis and Sadahiro Saeki PDF

Proc. Amer. Math. Soc. 100 (1987), 271-274 Request permission

Abstract:

A condition is given on the invertible elements of a commutative Banach algebra $\mathbf {B}$ which implies that the radical of $\mathbf {B}$ is not complemented by any closed subalgebra. This condition is then applied to show that certain quotient algebras of group algebras have an uncomplemented radical.

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Extension of a theorem of Henry Helson