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International Journal of Mathematics and Mathematical Sciences
Volume 13, Issue 1, Pages 135-138

A note on one-parameter groups of automorphisms

Department of Mathematics, Quiad-i-Azam University, Islamabad, Pakistan

Received 7 July 1988; Revised 1 September 1988

Copyright © 1990 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Let {αt:tR} and {βt:tR} be two commuting one-parameter groups of -automorphisms of a von Neumann algebra M such that αt+αt=βt+βt for all tR. The purpose of this note is to provide a simple and short proof of the central decomposition result: αt=βt on Mp and a αt=βt on M(1p) for a central projection pM, without using the theory of spectral subspaces.