J. Aust. Math. Soc.
81 (2006), 279295

Automatic continuity for Banach algebras with finitedimensional radical


Abstract

The paper \cite{dalesloy1997} proved a necessary
algebraic condition for a Banach algebra
with finitedimensional radical
to have a unique complete (algebra) norm, and
conjectured that this condition is also
sufficient. We extend the above theorem. The
conjecture is confirmed in the case where
is separable and
is commutative, but is shown to fail in general.
Similar questions for derivations are discussed.

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