Weakly ordered partial commutative group of self-adjoint linear operators densely defined on Hilbert space

Abstract

We continue in a direction of describing an algebraic structure
of linear operators on infinite-dimensional complex Hilbert space H.
In [6] Paseka and Janda introduced the notion of a weakly ordered
partial commutative group and showed that linear operators on H
with restricted addition possess this structure. In our work, we are
investigating the set of self-adjoint linear operators on H showing that
with more restricted addition it also has the structure of a weakly
ordered partial commutative group.