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

Acta Polytechnica

Jirí Janda¹ 

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

DOI  :  

来源: Czech Technical University in Prague, Faculty of M

【 摘 要 】

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.

【 授权许可】

Unknown