C^∗-algebras with approximately inner flip

Edward George Effros and Jonathan Rosenberg

Vol. 77 (1978), No. 2, 417–443

DOI: 10.2140/pjm.1978.77.417

Abstract

A remarkable recent theorem of A. Connes shows that if N is a II₁ factor on a separable Hilbert space, the “flip automorphism” of N ⊗ N can be approximated pointwise by inner automorphisms if and only if N is hyperfinite. We have accordingly been led to consider the analogous question of when, for a C^∗-algebra A, the “flip” on A ⊗ A (C^∗-rather than W^∗-tensor product) is “approximately inner.” We find that under certain additional hypotheses, A must be UHF (if A has a unit) or matroid (if we allow nonunital algebras).

Mathematical Subject Classification 2000

Primary: 46L05

Milestones

Received: 1 December 1977

Published: 1 August 1978