Mathematische Annalen

, Volume 374, Issue 1–2, pp 273–322 | Cite as

A \(C^*\)-algebraic approach to the principal symbol II

  • Edward McDonaldEmail author
  • Fedor Sukochev
  • Dmitriy Zanin


We introduce an abstract theory of the principal symbol mapping for pseudodifferential operators extending the results of Sukochev and Zanin (J Oper Theory, 2019) and providing a simple algebraic approach to the theory of pseudodifferential operators in settings important in noncommutative geometry. We provide a variant of Connes’ trace theorem which applies to certain noncommutative settings, with a minimum of technical preliminaries. Our approach allows us to consider operators with non-smooth symbols, and we demonstrate the power of our approach by extending Connes’ trace theorem to operators with non-smooth symbols in three examples: the Lie group \(\mathrm {SU}(2)\), noncommutative tori and Moyal planes.



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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Edward McDonald
    • 1
    Email author
  • Fedor Sukochev
    • 1
  • Dmitriy Zanin
    • 1
  1. 1.University of New South Wales SydneySydneyAustralia

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