Weakly Ordered A-Commutative Partial Groups of Linear Operators Densely Defined on Hilbert Space
DOI:
https://doi.org/10.14311/1807Keywords:
(generalized) effect algebra, partial group, weakly ordered partial group, Hilbert space, unbounded linear operator, self-adjoint linear operatorAbstract
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.Downloads
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