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PreprintCC BY 4.0arXiv

Rapid decay and functional calculus in C*-probability spaces

  • Felipe Flores
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Abstract

Let (A,ρ) be a tracial C*-probability space with the rapid decay property relative to a filtration L. We show that the associated Sobolev algebra HL∞(A,ρ) is closed under the smooth functional calculus of A. Some consequences include norm estimates, the ideal separation property, and the fact that the inclusion HL∞(A,ρ)⊂ A induces an isomorphism in K-theory.

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Cite

BibTeXRIS
BibTeX
@misc{flores2026rapid,
  title = {{Rapid decay and functional calculus in $\rm C^*$-probability spaces}},
  author = {Felipe Flores},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.00452},
  eprint = {2609.00452},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.00452},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Rapid decay and functional calculus in C^*-probability spaces
AU  - Felipe Flores
PY  - 2026
DA  - 2026/09/01
PB  - arXiv
DO  - 10.48550/arxiv.2609.00452
UR  - https://arxiv.org/abs/2609.00452
AB  - Let (A,ρ) be a tracial C^*-probability space with the rapid decay property relative to a filtration L. We show that the associated Sobolev algebra H_L^∞(A,ρ) is closed under the smooth functional calculus of A. Some consequences include norm estimates, the ideal separation property, and the fact that the inclusion H_L^∞(A,ρ)⊂ A induces an isomorphism in K-theory.
ER  -