The Douglas lemma for von Neumann algebras and some applications
Advances in Operator Theory
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.
Nayak, Soumyashant, "The Douglas lemma for von Neumann algebras and some applications" (2021). Journal Articles. 1893.
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