Quantum differentiability – the analytical perspective

  • E. McDonald
  • , F. Sukochev*
  • , X. Xiong
  • *Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

The study of quantum differentiability (in the sense of Connes) concerns the characterisation of the singular value sequences of commutators of pointwise multipliers with signs of Dirac operators. This subject ties together several themes in operator theory and harmonic analysis, and is inspired by analytic issues arising from cyclic cohomology and noncommutative differential geometry. We give a unified treatment of some recent results in this area, and a proof of the novel result that the necessary and sufficient conditions for quantum differentiability in noncommutative Euclidean spaces are formally identical to those of commutative Euclidean spaces.

Original languageEnglish
Title of host publicationCyclic Cohomology at 40
Subtitle of host publicationAchievements and Future Prospects
EditorsAlain Connes, Alain Connes, Caterina Consani, Bjørn Ian Dundas, Masoud Khalkhali, Henri Moscovici
PublisherAmerican Mathematical Society
Pages257
Number of pages1
ISBN (Print)9781470469771
DOIs
StatePublished - 2023
EventVirtual Conference on Cyclic Cohomology at 40: Achievements and Future Prospects, 2021 - Virtual, Online
Duration: 27 Sep 20211 Oct 2021

Publication series

NameProceedings of Symposia in Pure Mathematics
Volume105
ISSN (Print)0082-0717
ISSN (Electronic)2324-707X

Conference

ConferenceVirtual Conference on Cyclic Cohomology at 40: Achievements and Future Prospects, 2021
CityVirtual, Online
Period27/09/211/10/21

Keywords

  • Quantised derivative
  • Sobolev space
  • quantum Euclidean spaces
  • quantum tori
  • trace formula

Fingerprint

Dive into the research topics of 'Quantum differentiability – the analytical perspective'. Together they form a unique fingerprint.

Cite this