# \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.