A unified framework for the algebra of unsharp quantum mechanics
type: Item
instance of: scholarly article
title: A unified framework for the algebra of unsharp quantum mechanics
zbMATH Open document ID: 0898.03022
DOI: 10.1007/BF02435730
author: G. Cattaneo
published in: International Journal of Theoretical Physics
publication date: 1998-10-20T00:00:00Z
review text: The aim of the paper is to provide a common general framework for unsharp algebras for both classical and quantum propositional logics. For this purpose very general structures, so-called sum Brouwer-Zadeh algebras (SBZ-algebras) are introduced. Examples for such algebras are the real unit interval \([0,1]\) with truncated sum, the algebra of all fuzzy subsets of a fixed set, measurable spaces, the algebra of all effect operators on a Hilbert space and the algebra of all closed subspaces of a Hilbert space. Also structures similar to SBZ-algebras as well as observables, states, different kinds of orthogonality, sharp and unsharp elements, connections to logic and quantum and classical SBZ-algebras of effects are investigated. It is shown that any unsharp element can be approximated by a pair of sharp elements, one of them approximating the unsharp element from the bottom and the other from the top.
Mathematics Subject Classification ID: 03G12
Mathematics Subject Classification ID: 81P10
Mathematics Subject Classification ID: 06C15
zbMATH DE Number: 1161946
zbMATH Keywords: sum Brouwer-Zadeh algebra
zbMATH Keywords: fuzzy set
zbMATH Keywords: measurable space
zbMATH Keywords: effect operator
zbMATH Keywords: Hilbert space
zbMATH Keywords: closed subspace
zbMATH Keywords: observable
zbMATH Keywords: state
zbMATH Keywords: orthogonality
zbMATH Keywords: unsharp algebras
zbMATH Keywords: unsharp elements
zbMATH Keywords: sharp elements
reviewed by: Helmut Länger
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02435730
OpenAlex ID: W2011168879
description: scientific article; zbMATH DE number 1161946