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

Ilwoo Cho
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Ilwoo Cho: Department of Mathematics, Saint Ambrose University, 421 Ambrose Hall, 518 W. Locust St., Davenport, IA 52803, USA

Mathematics, 2017, vol. 5, issue 4, 1-37

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.

Keywords: free probability; Banach ?-probability spaces; von Neumann algebras; projections; semicircular elements; free filterizations; affiliated free filterizations (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2017
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