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- W2339968763 abstract "A bounded operator T on a Hilbert spaceH is said essentially normal when T ∗T−TT ∗ is a compact operator. Two operators are said unitarily equivalent modulo the compact operators when one is unitarily equivalent to a compact perturbation of the other. The goal of this work is to prove a theorem, that gives necessary and sufficient conditions for any two given essentially normal operators to be unitarily equivalent modulo the compact operators. In order to reach this objective, we will develop the BrownDouglas-Fillmore theory, that gives us a covariant functor on the category of compact metric spaces to the category of abelian groups, called the Ext functor, and a natural transformation that, to each compact metric space X, gives a group homomorphism γX : Ext(X) −→ Hom(π(X),Z), where π(X) denotes the first cohomotopy group of X. The classification theorem for essentially normal operators will follow from the fact that γX is a group isomorphism when X is a compact subset of the complex plane C." @default.
- W2339968763 created "2016-06-24" @default.
- W2339968763 creator A5035866365 @default.
- W2339968763 date "2005-01-01" @default.
- W2339968763 modified "2023-09-23" @default.
- W2339968763 title "Operadores essencialmente normais e a teoria de Brown-Douglas-Fillmore" @default.
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