# Operator algebra seminar

**Speaker:** James Gabe, KU

**Title:** Absorbing representations with respect to operator convex cones

**Abstract:** Let A be a separable, unital C*-algebra. One of the millions of ways of expressing Voiculescu's Weyl-von Neumann type theorem is the following: Any unital, faithful, essential representation of A on a separable, infinite dimensional Hilbert space absorbs any unital representation on a separable Hilbert space. Kirchberg showed that if one replaces B(H) above with the multiplier algebra of a sigma-unital, stable, simple, purely infinite C*-algebra B then we obtain a very similar result: Any unital, faithful, essential representation of A on M(B) absorbs any unital representation on M(B) which is weakly nuclear.

One could now ask the question: Let A be separable, unital, and let B be sigma-unital, stable. When can we find classes C of c.p. maps from A to B, and some (minimal) condition (C) such that we obtain the following: Any unital representation of A on M(B) satisfying (C) absorbs any unital representation on M(B) which is weakly in C. We discuss this problem, and give solutions in special cases, for certain "nice classes" C of operator convex cones.