Formal topology and constructive mathematics: the Gelfand and Stone-Yosida representation theorems
Abstract
Description
We present a constructive proof of the Stone-Yosida representation theorem for Riesz spaces motivated by considerations from formal topology. This theorem is used to derive a representation theorem for f-algebras. In turn, this theorem implies the Gelfand representation theorem for C*-algebras of operators on Hilbert spaces as formulated by Bishop and Bridges. Our proof is shorter, clearer, and we avoid the use of approximate eigenvalues.
This is an expanded version of our paper [CS05a]. For the convenience of the reader we have included more details and added a few clarifications. There are no new results. We are grateful to Bob Lubarsky and Fred Richman for suggesting improvements in the presentation
This is an expanded version of our paper [CS05a]. For the convenience of the reader we have included more details and added a few clarifications. There are no new results. We are grateful to Bob Lubarsky and Fred Richman for suggesting improvements in the presentation