Observables on Effect Algebras

讲座内容：Byan observable, we mean a σ-additive effect algebraic morphism from the Borelσ-algebra B(R) to a monotone σ-complete effect algebra E. It is straightforwardalgebraic generalization of a positive operator valued measure, hence itssignificance originates in a quantum measurement theory. Although observableswere studied from the beginning of effect algebraic research, in the recentyears, A. Dvurecenskij and M. Navarova introduced new approach to this fieldincluding several new techniques. Namely, they described the concept of aspectral resolution of an observable and its close connection with ageneralization of Loomis-Sikorsky theorem for effect algebras with RDP. Usingthe spectral resolution, A. Dvurecenskij described the so called Olson's order whichis a partial order on the set of observables. He also introduced a semigroupstructure on the set of observables in the the case when effect algebra E formsa complete distributive lattice. Our aim is to investigate the variousproperties of this partially ordered semigroup structure.