Workshop in Analysis and Probability Seminar

Date: July 30, 2014

Time: 4:00PM - 5:00PM

Location: Blocker 163

Speaker: Robert Pluta, Sam Houston State University

Title: Noncommutative retracts

Abstract: A subalgebra S of an algebra A is called a corner of A if there is an S-bimodule M contained in A such that A = S + M (direct sum of S-bimodules). Of course the prime example is the Peirce corner S = eAe associated with an idempotent e in A, but the above definition is more general and makes no reference to idempotents. In the first part of this presentation we will give a number of basic results about corners of general algebras and C*-algebras, partly surveying [1]. In the second part we will be concerned with closed and self-adjoint corners of C*-algebras that are complemented by ideals - a notion which we consider as a noncommutative analog of topological retracts. [1] R. Pluta, Ranges of Bimodule Projections and Conditional Expectations, Cambridge Scholars Publishing, 2013.