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

Jirí Janda

Abstract


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.

Keywords


(generalized) effect algebra; partial group; weakly ordered partial group; Hilbert space; unbounded linear operator; self-adjoint linear operator

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ISSN 1210-2709 (Print)
ISSN 1805-2363 (Online)
Published by the Czech Technical University in Prague