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Proceedings of the American Mathematical Society

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On local representations of von Neumann algebras


Author: Florin Pop
Journal: Proc. Amer. Math. Soc. 132 (2004), 3569-3576
MSC (2000): Primary 46L10, 46K10
Published electronically: July 22, 2004
MathSciNet review: 2084078
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Abstract: We prove that every bounded, linear, 2-local Hilbert space representation of a von Neumann algebra is a representation. In contrast, 1-local representations may fail to be multiplicative, even at the 2 by 2 matrix algebra level.


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Additional Information

Florin Pop
Affiliation: Department of Mathematics and Computer Science, Wagner College, Staten Island, New York 10301
Email: fpop@wagner.edu

DOI: https://doi.org/10.1090/S0002-9939-04-07585-9
Received by editor(s): February 3, 2003
Received by editor(s) in revised form: May 22, 2003
Published electronically: July 22, 2004
Communicated by: David R. Larson
Article copyright: © Copyright 2004 American Mathematical Society