Finite-dimensional representations and AF mapping telescopes

Kristin Courtney (University of Virginia)

Thursday 25th January 16:00-17:00 Maths 311B

Abstract

A residually finite-dimensional (RFD) C*-algebra is one for which the norm of every element equals the supremum of its norms under finite-dimensional representations. We consider the set of elements for which this supremum is a maximum: when is it dense, and when is it equal to the whole algebra? To answer the latter question, we develop a technique utilizing the projectivity of AF mapping telescopes. It turns out that this technique can be adapted to prove a variety of results, several of which will be highlighted. This is joint work with Tatiana Shulman.

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