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Invariant subspaces and representations of certain von Neumann algebras


Authors: Tomoyoshi Ohwada, Guoxing Ji and Kichi-Suke Saito
Journal: Proc. Amer. Math. Soc. 129 (2001), 3501-3510
MSC (2000): Primary 46L10, 47L65; Secondary 46L40
DOI: https://doi.org/10.1090/S0002-9939-01-06273-6
Published electronically: June 27, 2001
MathSciNet review: 1715970
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Abstract:

Let $(N,\alpha ,G)$ be a covariant system and let $(\pi,U)$be a covariant representation of $(N,\alpha,G)$ on a Hilbert space $\mathcal{H}$. In this note, we investigate the representation of the covariance algebra $M$ and the $\sigma $-weakly closed subalgebra $\mathfrak{A}$ generated by $\pi (N)$ and $\{U_{g}\}_{g \geq 0}$ in the case of $G= \mathbb{Z} $ or $\mathbb{R} $ when there exists a pure, full, $\mathfrak{A}$-invariant subspace of $\mathcal{H}$.


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Additional Information

Tomoyoshi Ohwada
Affiliation: Department of Mathematics, General Education, Tsuruoka National College of Technology, Tsuruoka, 997–8511, Japan
Email: ohwada@tsuruoka-nct.ac.jp

Guoxing Ji
Affiliation: Department of Mathematics, Shaanxi Normal University, Xian, 710062, Shaanxi, People’s Republic of China
Email: gxji@dns.snnu.edu.cn

Kichi-Suke Saito
Affiliation: Department of Mathematics, Faculty of Science, Niigata University, Niigata, 950–21, Japan
Email: saito@math.sc.niigata-u.ac.jp

DOI: https://doi.org/10.1090/S0002-9939-01-06273-6
Received by editor(s): September 16, 1999
Published electronically: June 27, 2001
Additional Notes: This work was supported in part by a Grant-in-Aid for Scientific Research, Japan Society for Promotion of Science.
Communicated by: David R. Larson
Article copyright: © Copyright 2001 American Mathematical Society

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