ON THE FUNCTIONAL CALCULUS IN ARCHIMEDEAN RIESZ SPACES WITH APPLICATIONS TO APPROXIMATION THEOREMS

Abstract

We show that the functional calculus defined on the class of Dedekind σ-complete Riesz spaces can be extended to the class of uniformly complete Archimedean Riesz spaces without representing in the process the spaces involved by spaces of functions. As a consequence some results in the theory of Riesz spaces which were proved previously by representation techniques, can now be proved in an intrinsic way.