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
In this paper, we construct a free semicircular family induced by
-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.
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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MDPI and ACS Style
Cho, I. Acting Semicircular Elements Induced by Orthogonal Projections on Von-Neumann-Algebras. Mathematics 2017, 5, 74.
Cho I. Acting Semicircular Elements Induced by Orthogonal Projections on Von-Neumann-Algebras. Mathematics. 2017; 5(4):74.
Cho, Ilwoo. 2017. "Acting Semicircular Elements Induced by Orthogonal Projections on Von-Neumann-Algebras." Mathematics 5, no. 4: 74.
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