Professors Curtis and Bade will continue their research into the underlying structural relationship between the radical in a non-semisimple Banach algebra and the algebra which contains it. This problem will be pursued in the context of amenable or weakly amenable Banach algebras. Particular attention will be paid to non-semisimple algebras arising from sets of non spectral synthesis for group algebras of locally compact abelian groups and for the associated Beurling algebras. Banach algebras are composed of abstract objects which can be added or multiplied, but the exact form of the multiplication rule is purposely not specified so that the results obtained apply to very many situations. Concrete examples of Banach algebras are plentiful, and this research will help elucidate their structure.
