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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Automorphism of von Neumann algebras as point transformations


Author: Charles Radin
Journal: Proc. Amer. Math. Soc. 39 (1973), 343-346
MSC: Primary 46L10
MathSciNet review: 0313829
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Abstract: Given a concrete separable $ {C^ \ast }$-algebra $ \mathfrak{A}$ with unit and a faithful normal finite trace $ \tau $ on $ \mathfrak{A}''$, we introduce a notion of $ \tau $-almost every state on $ \mathfrak{A}$ which has the proper relationship with Segal's noncommutative integration theory. We then prove that any $ \ast $-automorphism of $ \mathfrak{A}''$ is implemented by some point transformation in the state space of $ \mathfrak{A}$, defined $ \tau $-almost everywhere. This generalizes the classical result of von Neumann-Maharam.


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DOI: https://doi.org/10.1090/S0002-9939-1973-0313829-9
Keywords: Automorphisms of measure algebras, noncommutative integration
Article copyright: © Copyright 1973 American Mathematical Society