Computable Gelfand Duality

2024/02/26 by Peter Burton, Christopher J. Eagle, Burton, Peter +13
Computer Science · #03D45 #03D78 #46LO5 #Computability, Logic, AI Algorithms #FOS: Mathematics #Functional Analysis (math.FA) #Logic (math.LO)

paper · pdf · doi:10.48550/arxiv.2402.16672

openalex publication_date 2024/02/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

We establish a computable version of Gelfand Duality. Under this computable duality, computably compact presentations of metrizable spaces uniformly effectively correspond to computable presentations of unital commutative C^* algebras.

Related

• Constructive Gelfand duality for C*-algebras
• Evaluative presentations
• Constructive Gelfand duality for non-unital commutative C*-algebras
• Noncommmutative Gelfand Duality for not necessarily unital C^*-algebras, Jordan Canonical form, and the existence of invariant subspaces
• Totally Disconnected (non-metric) Gelfand Duality