Direct sums of tensor products and non-commutative independence
type: Item
instance of: scholarly article
title: Direct sums of tensor products and non-commutative independence
zbMATH Open document ID: 0868.46048
author: Michael Schürmann
published in: Journal of Functional Analysis
publication date: 1997-08-18T00:00:00Z
review text: The classical probability theory corresponds to commutative *-algebras and in this case two sub-*-algebras are independent in the state \(\Phi\) if in some sense the value of the state on the tensor product of restrictions is equal to the tensor product of the values of the state on each of its restrictions. These facts can be generalized into the non-commutative case in replacing tensor products by free products of *-algebras. The author has outlined the close ``connection between three known fundamental notions of non-commutative independence in quantum probability and the three basic choices for forming an associative direct sum of alternating tensor products of two vector spaces''.
reviewed by: Do Ngoc Diep
Mathematics Subject Classification ID: 46L80
Mathematics Subject Classification ID: 46M20
Mathematics Subject Classification ID: 81S25
zbMATH DE Number: 850597
zbMATH Keywords: noncommutative independence
zbMATH Keywords: free products of *-algebras
zbMATH Keywords: non-commutative independence
zbMATH Keywords: quantum probability
zbMATH Keywords: associative direct sum of alternating tensor products
MaRDI profile type: Publication
full work available at URL: jfan.1995.1114
OpenAlex ID: W1967438667
DOI: 10.1006/JFAN.1995.1114
description: scientific article; zbMATH DE number 850597