Non-Commutative Residue and Dixmier Trace

  • Fabio Nicola
  • Luigi Rodino
Part of the Pseudo-Differential Operators book series (PDO, volume 4)


Let us recall the following definition, valid for any algebra \( \mathcal{A} \) over ℂ. Definition 5.0.1. The linear map τ: \( \mathcal{A} \to \mathbb{C} \) is called a trace if it vanishes on commutators, i.e., if
$$ \tau \left( {\left[ {P,Q} \right]} \right) = \tau \left( {\left[ {PQ - QP} \right]} \right) = 0 for all P,Q \in \mathcal{A}. $$


Asymptotic Expansion Compact Operator Compact Manifold Symbolic Calculus Classical Symbol 
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Copyright information

© Springer Basel AG 2010

Authors and Affiliations

  • Fabio Nicola
    • 1
  • Luigi Rodino
    • 2
  1. 1.Dipartimento di MatematicaPolitecnico di TorinoTorinoItaly
  2. 2.Dipartimento di MatematicaUniversità di TorinoTorinoItaly

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