Sequential products on effect algebras
type: Item
instance of: scholarly article
title: Sequential products on effect algebras
zbMATH Open document ID: 1023.81001
DOI: 10.1016/S0034-4877(02)80007-6
published in: Reports on Mathematical Physics
publication date: 2002-10-21T00:00:00Z
review text: A measurement composed of two measurements represented by operation \(A,B\) is considered. The authors introduce axiomatically a more general notion of sequential product on an effect algebra and study its properties. The two elements \(A,B\) are called sequentially independent if \(A\circ B=B\circ A\). The relation between this property and compatibility is clarified. The sequential center is the set of elements which are sequentially independent to all other elements; it coincides with the set of sharp central elements. The case when the sequential center is isomorphic to a fuzzy set system is characterized. The existence of a sequential product appears to be a strong restriction. Boolean algebras are the only finite effect algebras admitting a sequential product. If a map preserves the sequential product then it completely preserves the effect algebra structure of the sharp elements. The existence of horizontal sums is characterized and some examples of horizontal sums and tensor products are given.
reviewed by: Mirko Navara
Mathematics Subject Classification ID: 81P15
Mathematics Subject Classification ID: 81P10
Mathematics Subject Classification ID: 03E72
Mathematics Subject Classification ID: 06C15
zbMATH DE Number: 1786202
zbMATH Keywords: effect algebra
zbMATH Keywords: sequential product
zbMATH Keywords: Hilbert space operator
zbMATH Keywords: fuzzy set
zbMATH Keywords: horizontal sums
zbMATH Keywords: tensor products
author: Stan Gudder
author: Richard J. Greechie
MaRDI profile type: Publication
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full work available at URL: s0034-4877(02)80007-6
OpenAlex ID: W2077498699
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description: scientific article; zbMATH DE number 1786202