Completeness of symmetric $\varDelta $-normed spaces of $\tau $-measurable operators
Volume 237 / 2017
Studia Mathematica 237 (2017), 201-219
MSC: Primary 46L10; Secondary 46E30.
DOI: 10.4064/sm8349-10-2016
Published online: 3 March 2017
Abstract
Let ${\mathcal M}$ be an arbitrary semifinite von Neumann algebra equipped with a faithful normal semifinite trace $\tau $ and let $E$ be a complete symmetric $\varDelta $-normed function space. We show that the corresponding symmetric space $E({\mathcal M},\tau )$ of $\tau $-measurable operators in $S({\mathcal M},\tau )$ is a complete symmetrically $\varDelta $-normed ideal.
