PreprintCC BY 4.0arXiv
The computable functional calculus
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 C*-algebra, the existence of effective approximate units for computably presented C*-algebras, and an effective version of the Spectral Theorem for compact operators on separable Hilbert spaces.
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BibTeX
@misc{eagle2026computable,
title = {{The computable functional calculus}},
author = {Christopher J. Eagle and Timothy H. McNicholl},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2606.05456},
eprint = {2606.05456},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.05456},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - The computable functional calculus
AU - Christopher J. Eagle
AU - Timothy H. McNicholl
PY - 2026
DA - 2026/10/22
PB - arXiv
DO - 10.48550/arxiv.2606.05456
UR - https://arxiv.org/abs/2606.05456
AB - 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 C^*-algebra, the existence of effective approximate units for computably presented C^*-algebras, and an effective version of the Spectral Theorem for compact operators on separable Hilbert spaces.
ER -