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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Spatially induced groups of automorphisms of certain von Neumann algebras


Author: Robert R. Kallman
Journal: Trans. Amer. Math. Soc. 156 (1971), 505-515
MSC: Primary 46.65; Secondary 81.00
MathSciNet review: 0275180
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Abstract: This paper gives an affirmative solution, in a large number of cases, to the following problem. Let $ \mathcal{R}$ be a von Neumann algebra on the Hilbert space $ \mathcal{H}$, let G be a topological group, and let $ a \to \varphi (a)$ be a homomorphism of G into the group of $ ^ \ast $-automorphisms of $ \mathcal{R}$. Does there exist a strongly continuous unitary representation $ a \to U(a)$ of G on $ \mathcal{H}$ such that each $ U(a)$ induces $ \varphi (a)$?


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DOI: http://dx.doi.org/10.1090/S0002-9947-1971-0275180-8
PII: S 0002-9947(1971)0275180-8
Keywords: von Neumann algebras, operator algebras, groups of automorphisms, quantum mechanics
Article copyright: © Copyright 1971 American Mathematical Society