Kurt Gödel Research Center

2010 seminar talk: Intro to operator algebras, II

Talk held by Asger Törnquist (KGRC) at the KGRC seminar on 2010-01-21.

Abstract

Today I will outline a proof of a result of Akemann and Weaver from 2004 that Diamond implies that there is a unital C* algebra generated by aleph_1 elements, which has the property that all irreducible representations (irreps) are equivalent (i.e. unitarily conjugate.) This shows the consistency of a negative solution to a problem posed by Naimark in 1948, asking if K(H) is the only C* algebra with the property that all irreps are equivalent. (In that 1948 paper Naimark showed that all irreps of K(H) are equivalent, hence the question.)