Algebra Seminar talk

Zdenka Riecanova
Operator Effect algebras in Hilbert spaces

We show that the set of all positive linear operators densely defined in an infinite-dimensional complex Hilbert space can be equiped with partial sum of operators making it a generalized effect algebra. This sum coincides with the usual sum of two operators whenewer this sum exists. Moreover, blocks of these generalized effect algebras are maximal sub-generalized effect algebras. All intervals in this generalized effect algebra become effect algebras which are Archimedean, convex, interval effect algebras, for which the set of vector states are order determining. Further, these interval operator effect algebras posess also faithful states.