Professor Thomas will conduct research in the area of non- commutative Banach algebras. His main goal is to prove a version of the Singer-Wermer conjecture generalizing his previous result proved in the commutative case. In addition he will study the structure theory of radicals in Banach algebras. Banach algebras consist of abstract objects which can be added and multiplied, but the exact form of the multiplication rule is purposely left unspecified 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.
