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

Author

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  • Ilwoo Cho

    (Department of Mathematics, Saint Ambrose University, 421 Ambrose Hall, 518 W. Locust St., Davenport, IA 52803, USA)

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.

Suggested Citation

  • Ilwoo Cho, 2017. "Acting Semicircular Elements Induced by Orthogonal Projections on Von-Neumann-Algebras," Mathematics, MDPI, vol. 5(4), pages 1-37, December.
    • Handle: RePEc:gam:jmathe:v:5:y:2017:i:4:p:74-:d:121915
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