Spatially induced groups of automorphisms of certain von Neumann algebras

Kallman, Robert R.

doi:10.1090/S0002-9947-1971-0275180-8

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
DOI: https://doi.org/10.1090/S0002-9947-1971-0275180-8
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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