Vol. 57, No. 2, 1975

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Groups of -automorphisms and invariant maps of von Neumann algebras

Kazuyuki Saitô

Vol. 57 (1975), No. 2, 553–558

Let M be a von Neumann algebra and let G be a group acting on M by -automorphisms of M. M is G-finite if for every nonnegative element a in M with a0, there exists a G-invariant normal state ϕ such that ϕ(a)0. The main result in this paper asserts that M is G-finite if and only if for every weakly relatively compact subset K of the predual of M, the orbit of K under G is also weakly relatively compact.

Mathematical Subject Classification 2000
Primary: 46L10
Received: 4 March 1974
Revised: 3 March 1975
Published: 1 April 1975
Kazuyuki Saitô