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Mathematics 2017, 5(4), 74; https://doi.org/10.3390/math5040074

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
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)
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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. 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
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Cho, I. Acting Semicircular Elements Induced by Orthogonal Projections on Von-Neumann-Algebras. Mathematics 2017, 5, 74.

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