Intervals in Generalized Effect Algebras and their Sub-generalized Effect Algebras

Abstract

We consider subsets G of a generalized effect algebra E with 0∈G and such that every interval [0, q]G = [0, q]E ∩ G of G (q ∈ G , q ≠ 0) is a sub-effect algebra of the effect algebra [0, q]E. We give a condition on E and G under which every such G is a sub-generalized effect algebra of E.

Keywords

• generalized effect algebra
• effect algebra
• Hilbert space
• densely defined linear operators
• embedding
• positive operators valued state