Effect Algebras of Positive Self-adjoint Operators Densely Defined on Hilbert Spaces

We show that (generalized) effect algebras may be suitable very simple and natural algebraic structures for sets of (unbounded) positive self-adjoint linear operators densely defined on an infinite-dimensional complex Hilbert space. In these cases the effect algebraic operation, as a total or partially defined binary operation, coincides with the usual addition of operators in Hilbert spaces

Extensions of Effect Algebra Operations

We study the set of all positive linear operators densely defined in an infinite-dimensional complex Hilbert space. We equip this set with various effect algebraic operations making it a generalized effect algebra. Further, sub-generalized effect algebras and interval effect algebras with respect of these operations are investigated