The continuous functional calculus is computable, giving computable compactness of spectra, effective approximate units, and an effective spectral theorem for compact operators.
Non-computability of $K$-theory for computably presented C*-algebras
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abstract
We give an example of a unital C*-algebra $\mathbf{A}$ with a computable presentation and for which neither $K_0(\mathbf{A})$ nor $K_1(\mathbf{A})$ has a computable presentation.
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2026 1verdicts
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The computable functional calculus
The continuous functional calculus is computable, giving computable compactness of spectra, effective approximate units, and an effective spectral theorem for compact operators.