Formal topology and constructive mathematics: the Gelfand and Stone-Yosida representation theorems

Details Formal topology and constructive mathematics: the Gelfand and Stone-Yosida representation theorems Formal topology and constructive mathematics: the Gelfand and Stone-Yosida representation theorems

2008-08-20

arxiv.org/abs/0808.2705v1

Journal of Universal computation, volume 11, issue 12 2005

Mathematics

Functional Analysis

This is an expanded version of our paper [CS05a]. For the convenience of the reader we have included more details and added a

Scientific paper

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.

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