Essentially Normal Operators

  • Kenneth R. Davidson
Part of the Operator Theory Advances and Applications book series (OT, volume 207)


This is a survey of essentially normal operators and related developments. There is an overview of Weyl—von Neumann theorems about expressing normal operators as diagonal plus compact operators. Then we consider the Brown—Douglas—Fillmore theorem classifying essentially normal operators. Finally we discuss almost commuting matrices, and how they were used to obtain two other proofs of the BDF theorem.

Mathematics Subject Classification (2000)

47-02 47B15 46L80 


Essentially normal operator compact perturbation normal diagonal almost commuting matrices extensions of C*-algebras 


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Copyright information

© Springer Basel AG 2010

Authors and Affiliations

  • Kenneth R. Davidson
    • 1
  1. 1.Pure Math. Dept.University of WaterlooWaterlooCanada

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