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.

Other Information: 

PIMS Distinguished Lecture 2007