Weakly Ordered A-Commutative Partial Groups of Linear Operators Densely Defined on Hilbert Space

The notion of a generalized effect algebra is presented as a generalization of effect algebra for an algebraic description of the structure of the set of all positive linear operators densely defined on a Hilbert space with the usual sum of operators. The structure of the set of not only positive li...

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Bibliographic Details
Published in:Acta polytechnica (Prague, Czech Republic : 1992) Vol. 53; no. 3
Main Author: Janda, Jirí
Format: Journal Article
Language:English
Published: CTU Central Library 01.01.2013
Subjects:
(generalized) effect algebra
Hilbert space
partial group
self-adjoint linear operator
unbounded linear operator
weakly ordered partial group
ISSN:1210-2709, 1805-2363
Online Access:Get full text
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Summary:The notion of a generalized effect algebra is presented as a generalization of effect algebra for an algebraic description of the structure of the set of all positive linear operators densely defined on a Hilbert space with the usual sum of operators. The structure of the set of not only positive linear operators can be described with the notion of a weakly ordered partial commutative group (wop-group).Due to the non-constructive algebraic nature of the wop-group we introduce its stronger version called a weakly ordered partial a-commutative group (woa-group). We show that it also describes the structure of not only positive linear operators.
ISSN:1210-2709
1805-2363
DOI:10.14311/1807