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- Title
Acting Semicircular Elements Induced by Orthogonal Projections on Von-Neumann-Algebras.
- Authors
Ilwoo Cho
- Abstract
In this paper, we construct a free semicircular family induced by |Z|-many mutually-orthogonal projections, and construct Banach *-probability spaces containing the family, called the free filterizations. By acting a free filterization on fixed von Neumann algebras, we construct the corresponding Banach *-probability spaces, called affiliated free filterizations. We study free-probabilistic properties on such new structures, determined by both semicircularity and free-distributional data on von Neumann algebras. In particular, we study how the freeness on free filterizations, and embedded freeness conditions on fixed von Neumann algebras affect free-distributional data on affiliated free filterizations.
- Subjects
VON Neumann algebras; ORTHOGONAL systems; BANACH spaces; FREE probability theory; DISTRIBUTION (Probability theory)
- Publication
Mathematics (2227-7390), 2017, Vol 5, Issue 4, p74
- ISSN
2227-7390
- Publication type
Article
- DOI
10.3390/math5040074