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\mathcal{PT}-Symmetry in (Generalized) Effect Algebras

Research paper by Jan Paseka

Indexed on: 27 Nov '10Published on: 27 Nov '10Published in: International Journal of Theoretical Physics



Abstract

We show that an η+-pseudo-Hermitian operator for some metric operator η+ of a quantum system described by a Hilbert space \({\mathcal{H}}\) yields an isomorphism between the partially ordered commutative group of linear maps on \({\mathcal{H}}\) and the partially ordered commutative group of linear maps on \({\mathcal{H}}_{\rho_{+}}\). The same applies to the generalized effect algebras of positive operators and to the effect algebras of c-bounded positive operators on the respective Hilbert spaces \({\mathcal{H}}\) and \({\mathcal{H}}_{\rho_{+}}\). Hence, from the standpoint of (generalized) effect algebra theory both representations of our quantum system coincide.