Maximality and finiteness of type 1 subdiagonal algebras

2020/03/29 by Ji, Guoxing
#46L52 #47L75 #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.2003.12966

Abstract

Let \mathfrak A be a type 1 subdiagonal algebra in a σ-finite von Neumann algebra \mathcal M with respect to a faithful normal conditional expectation Φ. We give necessary and sufficient conditions for which \mathfrak A is maximal among the σ-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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