Vol. 57, No. 2, 1975

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 327: 1
Vol. 326: 1  2
Vol. 325: 1  2
Vol. 324: 1  2
Vol. 323: 1  2
Vol. 322: 1  2
Vol. 321: 1  2
Vol. 320: 1  2
Online Archive
The Journal
Editorial Board
Submission Guidelines
Submission Form
Policies for Authors
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Special Issues
Author Index
To Appear
Other MSP Journals
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