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