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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Vydané v:	Acta polytechnica (Prague, Czech Republic : 1992) Ročník 53; číslo 3
Hlavný autor:	Janda, Jirí
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	CTU Central Library 01.01.2013
Predmet:	(generalized) effect algebra Hilbert space partial group self-adjoint linear operator unbounded linear operator weakly ordered partial group
ISSN:	1210-2709, 1805-2363
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Shrnutí:	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