Banach algebras of continuous functions and measures, and their second duals
Topic
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.
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.
Speakers
Additional Information
PIMS Distinguished Lecture 2007
Garth Dales (Leeds University)
Garth Dales (Leeds University)