Generalized Effect Algebras of Positive Self-adjoint Linear Operators on Hilbert Spaces

Abstract

In this paper, we introduce a partially defined binary operation on the set \(S^{+}(\mathcal {H})\) of all positive self-adjoint linear operators on a complex Hilbert space \(\mathcal {H}\), which makes the set into a generalized effect algebra. Moreover, we present two kinds of partial orders on \(S^{+}(\mathcal {H})\) and give the relationship of the two orders. We study two important topologies on \(S^{+}(\mathcal {H})\), too.