Journal of Operator Theory

Volume 39, Issue 2, Spring 1998 pp. 309-317.

Certain structure of subdiagonal algebras

Authors: Guoxing Ji (1), Tomoyoshi Ohwada (2), and Kichi-Suke Saito (3)
Author institution: (1) Department of Mathematical Science, Graduate School of Sci. and Technology, Niigata University, Niigata, 950-21, Japan
(2) Department of Mathematical Science, Graduate School of Sci. and Technology, Niigata University, Niigata, 950-21, Japan
(3) Department of Mathematics, Faculty of Science, Niigata University, Niigata, 950-21, Japan

Summary: subdiagonal algebra of a von Neumann algebra $\cal M$ with respect to a faithful normal expectation $\Phi$. Then we show that if $\varphi$ is a faithful normal state of $\cal M$ such that $\varphi \circ \Phi =\varphi$, then $\frak A$ is $\sigma_t^{\varphi}$-invariant, where $\{\sigma_t^{\varphi} \}_{t \in \bbb R}$ is the modular automorphism group associated with $\varphi$. As an application, we prove that every $ \sigma $-weakly closed subdiagonal algebra of ${\cal B} (\cal H)$ is a nest algebra with an atomic nest.

Keywords: von Neumann algebra, subdiagonal algebra

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