Invariant subspaces and representations of certain von Neumann algebras
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- by Tomoyoshi Ohwada, Guoxing Ji and Kichi-Suke Saito PDF
- Proc. Amer. Math. Soc. 129 (2001), 3501-3510 Request permission
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 $\mathcal {H}$.References
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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
- 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
- © Copyright 2001 American Mathematical Society
- 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
- MathSciNet review: 1715970