## Banach algebras of continuous functions and measures, and their second duals

- Date: 11/30/2007

Garth Dales (Leeds University)

University of Alberta

For every Banach algebra A, there are two products on the second dual

space A'' that make A'' into a Banach algebra; they may or may not

coincide. A lot of information about the original algebra A comes

easily by looking at these second duals. We shall first give the basic

definitions and some (old and new) examples.

The first detailed example is the case where A is C_0(Omega), an

algebra of continuous functions on a locally compact space Omega.

Next, let G be a locally compact group, and let L^1(G) and M(G) be the

group algebra and the measure algebra on G, respectively. We shall

describe the second duals L^1(G)'' and M(G)'', giving some classical

results, some new results, and some open questions.

PIMS Distinguished Lecture 2007