Reflexivity Of Murray-Von Neumann Algebras

Abstract

A Murray-von Neumann algebra Af (R) is the algebra of operators affiliated with a finite von Neumann algebra R. Such an algebra contains both bounded and unbounded operators on a Hilbert space. In this article, we study reflexivity of Murray-von Neumann algebras. We discuss the stability of closed subspaces of a Hilbert space H under closed, densely defined operators on H, based on which we define ̂LatS of a set S of closed, densely defined operators on H, and ÂlgP of a set P of closed subspaces of H. We show that Murray-von Neumann algebras Af (R) are reflexive, that is, Af (R) ≌ÂlĝLatAf (R). We also define ̂RefaAf (R), and show that Murray-von Neumann algebras Af (R) are algebraically reflexive, that is, Af (R) ≌̂RefaAf (R).

Publication Date

1-1-2016

Publication Title

Contemporary Mathematics

Volume

671

Number of Pages

175-184

Document Type

Article; Book Chapter

Personal Identifier

scopus

DOI Link

https://doi.org/10.1090/conm/671/13509

Socpus ID

85086065241 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/85086065241

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