Generalized effect algebras of positive operators densely defined on Hilbert spaces
type: Item
instance of: scholarly article
title: Generalized effect algebras of positive operators densely defined on Hilbert spaces
zbMATH Open document ID: 1237.81009
author: Marcel Polakovič
author: Z. Riečanová
published in: International Journal of Theoretical Physics
publication date: 2011-05-30T00:00:00Z
review text: Effect algebras have been introduced by \textit{D. J. Foulis} and \textit{M. K. Bennett} [``Effect algebras and unsharp quantum logics'', Found. Phys. 24, No. 10, 1331--1352 (1994; Zbl 1213.06004)] for modelling unsharp measurement in a quantum mechanical system. The authors of the paper under review consider examples of sets of positive linear operators defined on a dense linear subspace \(D\) in a (complex) Hilbert space \(\mathcal H\). Some of these operators may have a physical meaning in quantum mechanics. It is proved that the set of all positive linear operators with fixed such \(D\) and \(\mathcal H\) form a generalized effect algebra with respect to the usual addition of operators. Some sub-algebras are also mentioned. Moreover, on a set of all positive linear operators densely defined in an infinite dimensional complex Hilbert space, the partial binary operation is defined making this set a generalized effect algebra.
reviewed by: Michael Perelmuter
Mathematics Subject Classification ID: 81P10
Mathematics Subject Classification ID: 06C15
zbMATH DE Number: 5900903
zbMATH Keywords: quantum structures
zbMATH Keywords: (generalized) effect algebra
zbMATH Keywords: Hilbert space
zbMATH Keywords: (unbounded) positive linear operator
MaRDI profile type: Publication
full work available at URL: s10773-010-0458-3
OpenAlex ID: W2043322000
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DOI: 10.1007/S10773-010-0458-3
description: scientific article; zbMATH DE number 5900903