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arxiv: 2402.16672 · v2 · pith:DWT3EHH7new · submitted 2024-02-26 · 🧮 math.LO · math.FA

Computable Gelfand Duality

Peter Burton , Christopher J. Eagle , Alec Fox , Isaac Goldbring , Matthew Harrison-Trainor , Timothy H. McNicholl , Alexander Melnikov , Teerawat Thewmorakot This is my paper
classification 🧮 math.LO math.FA
keywords computabledualitygelfandpresentationsalgebrascommutativecompactcomputably
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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.

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  1. The computable functional calculus

    math.LO 2026-06 unverdicted novelty 5.0

    The continuous functional calculus is computable, giving computable compactness of spectra, effective approximate units, and an effective spectral theorem for compact operators.