Maximality and finiteness of type 1 subdiagonal algebras

Ji, Guoxing

doi:10.1090/proc/15287

Maximality and finiteness of type 1 subdiagonal algebras
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Proc. Amer. Math. Soc. 149 (2021), 1543-1554 Request permission

Abstract:

Let $\mathfrak A$ be a type 1 subdiagonal algebra in a $\sigma$-finite von Neumann algebra $\mathcal M$ with respect to a faithful normal conditional expectation $\Phi$. We give necessary and sufficient conditions for which $\mathfrak A$ is maximal among the $\sigma$-weakly closed subalgebras of $\mathcal M$. In addition, we show that a type 1 subdiagonal algebra in a finite von Neumann algebra is automatically finite which gives a positive answer of Arveson’s finiteness problem in 1967 in type 1 case.

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