2008•arXiv (Cornell University)Open access

Inclusions and positive cones of von Neumann algebras

Yoh Tanimoto

Abstract

We consider cones in a Hilbert space associated to two von Neumann algebras and determine when one algebra is included in the other. If a cone is assocated to a von Neumann algebra, the Jordan structure is naturally recovered from it and we can characterize projections of the given von Neumann algebra with the structure in some special situations.

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Key concepts: Von Neumann algebra, Abelian von Neumann algebra, Von Neumann architecture, Affiliated operator, Cone (formal languages), Jordan algebra, Hilbert space, Mathematics