# Algebra Seminar talk

2011-03-25

Zdenka **Riecanova***Operator Effect algebras in Hilbert spaces*

Abstract:

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.