Mathematical Sciences: Radical Banach Algebras

托马斯教授将在非交换巴拿赫代数领域进行研究。他的主要目标是证明Singer-Wermer猜想的一个版本，推广他之前在交换情况下证明的结果。此外，他将研究巴拿赫代数中根的结构理论。巴拿赫代数由可以相加和相乘的抽象对象组成，但乘法规则的确切形式故意不明确，以便得到的结果适用于很多情况。巴拿赫代数的具体例子很多，本研究将有助于阐明其结构。

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.