Analysis Seminar

Safoura Jafar-Zadeh, University of Manitoba

“Isometric Isomorphisms of Beurling Algebras Associated with Locally Compact Groups”

Weighted convolution algebras on the real line were introduced by Beurling and were sub- sequently defined on arbitrarily locally compact topological groups. Many works have since been devoted to the study of Beurling algebras (on locally compact groups). A natural ques- tion asks to what extent the algebraic structure of the weighted convolution Banach algebra L1(G, ω) determines the underlying weighted locally compact group (G, ω). This question was first raised and studied by Rudin when ω ≡ 1. It was observed by Wendel that, in general, the algebraic structure of the group algebra does not determine the underlying locally compact group. However, if we impose some restrictions on the algebraic isomorphism, success may be achieved. In this talk, I will show that the Banach algebraic structure of many Beurling algebras determines the underlying weighted locally compact group structure.

MC 5413