Weakly ordered partial commutative group of self-adjoint linear operators densely defined on Hilbert space
| Authors | |
|---|---|
| Year of publication | 2011 |
| Type | Article in Periodical |
| Magazine / Source | Tatra Mountains Mathematical Publications |
| MU Faculty or unit | |
| Citation | |
| Web | https://doi.org/10.2478/v10127-011-0037-x |
| Doi | http://dx.doi.org/10.2478/v10127-011-0037-x |
| Field | General mathematics |
| Keywords | (generalized) effect algebra; weakly ordered partial group; Hilbert sapce; unbounded linear operator; self-adjoint linear operator |
| Description | We continue in a direction of describing an algebraic structure of linear operators on infinite-dimensional complex Hilbert space H. In [Paseka, J.– –Janda, J.: More on PT-symmetry in (generalized) effect algebras and partial groups, Acta Polytech. 51 (2011), 65–72] there is introduced the notion of a weakly ordered partial commutative group and showed that linear operators on H with restricted addition possess this structure. In our work, we are investigating the set of self-adjoint linear operators on H showing that with more restricted addition it also has the structure of a weakly ordered partial commutative group. |
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