Lectures on Representation Theory for Banach Algebras and Locally Compact groups[MatSciRep:54]

Abstract

The aim of these lectures is to provide an introduction to some of the basic theorems of Representation theory. They are purely expository, there is little or nothing that cannot be found in standard treatises such as M.A. Naimark's normed rings or Volume 1 of 'Abstract Harmonic Analysis' by Hewitt and K.A. Ross. The background assumed is a) the Elementary theory of Banach Algebras, in particular of Commutative algebras upto Gelfand's Representation Theorem, b) The elementary theory of Haar Measure, on a locally compact group(not necessarily an abelian) c) standard results from linear analysis, such as spectral theorem, the Banach-Steinhaus theorem and the Krein-Milman theorem. This material is readily available in several excellant texts, and it would perhaps be superfluous to make specific recommendations.