Publication details
Intervals on weakly ordered partial commutative groups of linear operators
| Authors | |
|---|---|
| Year of publication | 2012 |
| Type | Article in Proceedings |
| Conference | Quantitative Logic and Soft Computing: Proceedings of the QL&SC 2012, Xian, China 12-15 May 2012 |
| MU Faculty or unit | |
| Citation | |
| Field | General mathematics |
| Keywords | (generalized) effect algebra; weakly ordered partial group; Hilbert space; unbounded linear operator; states; interval effect algebra |
| Description | The generalized effect algebra was 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 Hilbert space with the usual sum of operators. A structure of the set of not only positive linear operators can be described with the notion of weakly ordered partial commutative group (wop-group). With a restriction of the usual sum, the important subset of all self-adjoint operators forms a substructure of the set of all linear operators. We investigate the properties of intervals in wop-groups of linear operators and showing that they can be organised into effect algebras with nonempty set of states. |
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