Acting semicircular elements induced by orthogonal projections on von-Neumann-algebras
type: Item
instance of: scholarly article
title: Acting semicircular elements induced by orthogonal projections on von-Neumann-algebras
zbMATH Open document ID: 1398.46053
author: Ilwoo Cho
published in: Mathematics
publication date: 2018-07-05T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 46L54
zbMATH DE Number: 6898703
zbMATH Keywords: free probability
zbMATH Keywords: Banach \(*\)-probability spaces
zbMATH Keywords: von Neumann algebras
zbMATH Keywords: projections
zbMATH Keywords: semicircular elements
zbMATH Keywords: free filterizations
zbMATH Keywords: affiliated free filterizations
MaRDI profile type: Publication
full work available at URL: math5040074
OpenAlex ID: W2775221851
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DOI: 10.3390/MATH5040074
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description: scientific article; zbMATH DE number 6898703