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arXiv · 2606.05456

The computable functional calculus

Christopher J. Eagle·Timothy H. McNicholl
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Abstract

We show that the continuous functional calculus is computable. As consequences we obtain the computable compactness of the spectrum of any computable normal element of a computably presented $\mathrm{C}^*$-algebra, the existence of effective approximate units for computably presented $\mathrm{C}^*$-algebras, and an effective version of the Spectral Theorem for compact operators on separable Hilbert spaces.

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Christopher J. Eagle, Timothy H. McNicholl. 2026-06-03. The computable functional calculus. https://arxiv.org/abs/2606.05456

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