Vol. 77, No. 2, 1978

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Cāˆ—-algebras with approximately inner flip

Edward George Effros and Jonathan Rosenberg

Vol. 77 (1978), No. 2, 417ā€“443

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
Received: 1 December 1977
Published: 1 August 1978
Edward George Effros
Jonathan Rosenberg
Department of Mathematics
University of Maryland
College Park MD 20742-4015
United States