Vol. 76, No. 1, 1978

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Automorphisms of locally compact groups

Justin Peters and Terje Sund

Vol. 76 (1978), No. 1, 143–156

It is proved that for arbitrary locally compact groups G the automorphism group Aut (G) is a complete topological group. Several conditions equivalent to closedness of the group Int (G) of inner automorphisms are given, such as G admits no nontrivial central sequences. It is shown that Aut (G) is topologically embedded in the automorphism group Aut (G) of the group von Neumann algebra. However, closedness of Int (G) does not imply closedness of Int (G), nor conversely.

Mathematical Subject Classification 2000
Primary: 22D45
Received: 29 April 1977
Revised: 30 September 1977
Published: 1 May 1978
Justin Peters
Department of Mathematics
Iowa State University
Ames IA 50011
United States
Terje Sund