ON REALIZATION OF EFFECT ALGEBRAS
| Authors | |
|---|---|
| Year of publication | 2016 |
| Type | Article in Periodical |
| Magazine / Source | Mathematica Slovaca |
| MU Faculty or unit | |
| Citation | |
| Doi | http://dx.doi.org/10.1515/ms-2015-0140 |
| Field | General mathematics |
| Keywords | non-classical logics; orthomodular lattices; effect algebras; MV-algebras; states; simplex algorithm |
| Description | A well known fact is that there is a finite orthomodular lattice with an order determining set of states which is not order embeddable into the standard quantum logic, the lattice L(H) of all closed subspaces of a separable complex Hilbert space. We show that a finite generalized effect algebra is order embeddable into the standard effect algebra E(H) of effects of a separable complex Hilbert space iff it has an order determining set of generalized states iff it is order embeddable into the power of a finite MV-chain. As an application we obtain an algorithm, which is based on the simplex algorithm, deciding whether such an order embedding exists and, if the answer is positive, constructing it. (C) 2016 Mathematical Institute Slovak Academy of Sciences |
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