November 28, 2005
Ilan Hirshberg
Title: Introduction to Hilbert C*-modules and Pimsner algebras
This will be an introductory talk for nonspecialists. A Hilbert module (or Hilbert C*-module) is a generalization of a Hilbert space, where the scalars are taken to be elements of a C*-algebra. A C*-correspondence is a Hilbert C*-module, along with a way for the coefficient algebra to act on the module from the other side (thus making it a bimodule). Given such a bimodule stucture, one can form a far-reaching generalization of the Toeplitz algebra and a related quotient. This construction was introduced in an influential paper by Pimsner, and generalized several known and important examples in the theory. I hope to give the basic definitions, explain Pimsner's construction and some examples, and time permitting, give or sketch a proof that the Pimsner-Toeplitz algebra has a universal property with respet to representations of the C*-correspondence.