Spatially induced groups of automorphisms of certain von Neumann algebras-Reference-Cited by-同舟云学术

Spatially induced groups of automorphisms of certain von Neumann algebras

Published:1971 Issue:0 Volume:156 Page:505-515
ISSN:0002-9947
Container-title:Transactions of the American Mathematical Society
language:en
Short-container-title:Trans. Amer. Math. Soc.

Author:

Kallman Robert R.

Abstract

This paper gives an affirmative solution, in a large number of cases, to the following problem. Let R \mathcal {R} be a von Neumann algebra on the Hilbert space H \mathcal {H} , let G be a topological group, and let a → φ ( a ) a \to \varphi (a) be a homomorphism of G into the group of ∗ ^ \ast -automorphisms of R \mathcal {R} . Does there exist a strongly continuous unitary representation a → U ( a ) a \to U(a) of G on H \mathcal {H} such that each U ( a ) U(a) induces φ ( a ) \varphi (a) ?

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/tran/1971-156-00/S0002-9947-1971-0275180-8/S0002-9947-1971-0275180-8.pdf

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5. Measure Theory

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1. References;Von Neumann Algebras;1981

2. On groups of automorphisms of operator algebras;Mathematical Proceedings of the Cambridge Philosophical Society;1977-03

3. References;North-Holland Mathematical Library;1977

4. Sufficient conditions of covariance of represen'tations of C* algebras. II;Theoretical and Mathematical Physics;1973-11

5. Unitary implementation of automorphism groups on von Neumann algebras;Communications in Mathematical Physics;1972-12