Banach Algebras of continuous functions and measures, and their second duals

Start: 11/19/2007 - 3:15pm
End  : 11/19/2007 - 4:15pm


H.G. Dales (Leeds College, UK)


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 orginal 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_{\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 scond duals $ L^1(G)'' $ and $ M(G)'' $, giving some classical results, some new results, and some open questions.

Millikan 134 Pomona College

Misc. Information

Coffee & cookies at 4:00 p.m.
Wine and cheese after the talk.
Harry Mullikin Room, Millikan 209

The dinner will be hosted by Sandy Grabiner
If interested in attending, call Ext. 18707