This article is cited in 2 papers

Brief communications

Factorization Properties of Subdiagonal Algebras

T. N. Bekjan, K. N. Ospanov

L. N. Gumilev Eurasian National University

Abstract: Let $\mathcal{M}$ be a von Neumann algebra equipped with a normal finite faithful normalized trace $\tau$, and let $\mathcal{A}$ be a tracial subalgebra of $\mathcal{M}$. Let $E$ be a symmetric quasi-Banach space on $[0,1]$. We show that $\mathcal{A}$ has an $L_E(\mathcal{M})$-factorization if and only if $\mathcal{A}$ is a subdiagonal algebra.

Keywords: von Neumann algebra, tracial subalgebra, subdiagonal algebra, noncommutative symmetric space.

UDC: 517.986.3

Received: 20.05.2015

DOI: 10.4213/faa3234

 English version: Functional Analysis and Its Applications, 2016, 50:2, 146–149

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