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Acting Semicircular Elements Induced by Orthogonal Projections on Von-Neumann-Algebras

Department of Mathematics, Saint Ambrose University, 421 Ambrose Hall, 518 W. Locust St., Davenport, IA 52803, USA
Mathematics 2017, 5(4), 74; https://doi.org/10.3390/math5040074
Received: 18 September 2017 / Revised: 20 November 2017 / Accepted: 21 November 2017 / Published: 6 December 2017
(This article belongs to the Special Issue Mathematical Physics and Quantum Information)
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. View Full-Text
Keywords: free probability; Banach ∗-probability spaces; von Neumann algebras; projections; semicircular elements; free filterizations; affiliated free filterizations free probability; Banach ∗-probability spaces; von Neumann algebras; projections; semicircular elements; free filterizations; affiliated free filterizations
MDPI and ACS Style

Cho, I. Acting Semicircular Elements Induced by Orthogonal Projections on Von-Neumann-Algebras. Mathematics 2017, 5, 74.

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