Considerable Sets of Linear Operators in Hilbert Spaces as Operator Generalized Effect Algebras
| Authors | |
|---|---|
| Year of publication | 2011 |
| Type | Article in Periodical |
| Magazine / Source | Foundations of Physics |
| MU Faculty or unit | |
| Citation | |
| Web | http://www.springerlink.com/content/34h7p0018736878x/ |
| Doi | http://dx.doi.org/10.1007/s10701-011-9573-0 |
| Field | General mathematics |
| Keywords | Quantum structures; (Generalized) effect algebra; Hilbert space; (Unbounded) positive linear operator; Closure; Adjoint; Friedrichs extension |
| Description | We show that considerable sets of positive linear operators namely their extensions as closures, adjoints or Friedrichs positive self-adjoint extensions form operator (generalized) effect algebras. Moreover, in these cases the partial effect algebraic operation of two operators coincides with usual sum of operators in complex Hilbert spaces whenever it is defined. These sets include also unbounded operators which play important role of observables (e.g., momentum and position) in the mathematical formulation of quantum mechanics. |
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