Extensions of Effect Algebra Operations

Abstract

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.

Keywords

• generalized effect algebra
• effect algebra
• Hilbert space
• densely defined linear operators
• extension of operations