The Douglas lemma for von Neumann algebras and some applications

Article Type

Research Article

Publication Title

Advances in Operator Theory

Abstract

In this article, we discuss some applications of the well-known Douglas factorization lemma in the context of von Neumann algebras. Let B(H) denote the set of bounded operators on a complex Hilbert space H, and R be a von Neumann algebra acting on H. We prove some new results about left (or, one-sided) ideals of von Neumann algebras; for instance, we show that every left ideal of R can be realized as the intersection of a left ideal of B(H) with R. We also generalize a result by Loebl and Paulsen (Linear Algebra Appl 35:63–78, 1981) pertaining to C∗-convex subsets of B(H) to the context of R-bimodules.

DOI

10.1007/s43036-021-00143-4

Publication Date

7-1-2021

Comments

Open Access, Green

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