形式拓扑与构造性数学：Gelfand 与 Stone-Yosida 表示定理
泛函分析
2008-08-21 v1 逻辑
摘要
我们受形式拓扑的考量启发，给出了 Riesz 空间的 Stone-Yosida 表示定理的一个构造性证明。该定理用于推导 f-代数的表示定理。进而，该定理蕴含了由 Bishop 和 Bridges 表述的希尔伯特空间上算子 C*-代数的 Gelfand 表示定理。我们的证明更短、更清晰，并且避免使用近似特征值。
引用
@article{arxiv.0808.2705,
title = {Formal topology and constructive mathematics: the Gelfand and Stone-Yosida representation theorems},
author = {Thierry Coquand and Bas Spitters},
journal= {arXiv preprint arXiv:0808.2705},
year = {2008}
}
备注
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