Characterization of Subdiagonal Algebras on Noncommutative Lorentz Spaces

Abstract

Let \((M, \tau)\) be a finite von Neumann algebra, \(A\) be a tracial subalgebra of \(M\). We prove that \(A\) has \(L^{p,q}\)-factorization if and only if \(A\) is a subdiagonal algebra. We also obtain some characterizations of subdiagonal algebras.