As a natural generalization of partially ordered sets and Boolean
algebras, the effect algebras contain elements called ``events" that
may be pairwise incompatible (cf. the concept of MV lattices) and/or
``not sharp" (cf. the concept of orthomodular lattices). It is
believed that the effect algebras might provide ``the" language for
studying quantum structures and, in particular, the sets of positive
operators  that are densely defined on the pairs of Hilbert spaces
which differ just by their inner products. The mutual
physical-prediction equivalence between the latter Hilbert-space
pairs forms a basic ingredient in the version of quantum mechanics
nicknamed ``PT-symmetric" (hence the title of this paper, cf. the
review [10], with the updated volume 7 and page 1191, for more
details). In the paper under review the author shows and explains,
how and in which sense both the latter Hilbert-space representations
may be considered equivalent also from the point of view of the
(generalized) effect algebras.

MR2780961 Paseka, Jan $\scr{PT}$-symmetry in (generalized) effect
algebras. Internat. J. Theoret. Phys. 50 (2011), no. 4, 1198--1205.
81Qxx (06D35)