Analysis seminar

Matthew Mazowita, Department of Pure Mathematics, University of Waterloo

“Weights and topological centres”

If A is a Banach algebra, there are two products on the second dual A∗∗ which extend the product on A, called the Arens products. Their agreement is measured by the topological centres of A. The group algebra L1(G) always has minimal topological centres for any locally compact group G, whereas operator algebras always have maximal topological centres. If ω is a weight on G then we can form the weighted group (or Beurling) algebra, which can behave very differently than the (unweighted) group algebra. In this talk I will discuss the topological centre problem for Beurling and related algebras as well as a weighted analogue of the semigroup compactification GLUC of the group. I will also use these results to describe the isometric isomorphisms of Beurling algebras.