Order properties of bounded self-adjoint operators

Abstract

2 We adopt the notation: C'{X) for the set of all complex-valued continuous functions on the compact Hausdorff space X; C{X) for the set of real functions in C'{X); C'{Y) for the set of all complex-valued continuous functions vanishing at » on the locally compact Hausdorff space F; C(F) the set of real functions in C'{Y).X will always denote a compact Hausdorff space and Y a locally compact Hausdorff space.