Acting semicircular elements induced by orthogonal projections on von-Neumann-algebras (Q1649069)

Summary: In this paper, we construct a free semicircular family induced by \(|\mathbb Z|\)-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.