Invariant subspaces and representations of certain von Neumann algebras期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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Invariant subspaces and representations of certain von Neumann algebras

Authors:	Tomoyoshi Ohwada Guoxing Ji Kichi-Suke Saito

Institution:	Department of Mathematics, General Education, Tsuruoka National College of Technology, Tsuruoka, 997--8511, Japan ; Department of Mathematics, Shaanxi Normal University, Xian, 710062, Shaanxi, People's Republic of China ; Department of Mathematics, Faculty of Science, Niigata University, Niigata, 950--21, Japan

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 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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