Approximation with Normal Operators with Nite Spectrum, and an Elementary Proof of a Brown-douglas-fillmore Theorem
نویسنده
چکیده
We give a short proof of the theorem of Brown, Douglas and Fillmore that an essentially normal operator on a Hilbert space is a compact perturbation of a normal operator if and only if the Fredholm index of its translates are zero whenever deened. The proof is a modiication of the short proof of Lin's theorem on almost commuting self-adjoint elements we gave in 7]. Using similar methods we prove some new results, that generalize results of Lin, about when a normal element in a C-algebra can be approximated by normal elements with nite spectra.
منابع مشابه
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 t...
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