Invariant subspaces and representations of certain von Neumann algebras

Ohwada, Tomoyoshi; Ji, Guoxing; Saito, Kichi-Suke

doi:10.1090/S0002-9939-01-06273-6

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 $\mathcal {H}$.

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