Geodesic
Structure of spectra of linear operators in Banach spaces
Sbornik. Mathematics, Tome 192 (2001) no. 4, pp. 577-591

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Descriptive characterizations of the point, the continuous, and the residual spectra of operators in Banach spaces are put forward. In particular, necessary and sufficient conditions for three disjoint subsets of the complex plane to be the point spectrum, the continuous spectrum, and the residual spectrum of a linear continuous operator in a separable Banach space are obtained. 
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     author = {O. G. Smolyanov and S. A. Shkarin},
     title = {Structure of spectra of linear operators in {Banach} spaces},
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O. G. Smolyanov; S. A. Shkarin. Structure of spectra of linear operators in Banach spaces. Sbornik. Mathematics, Tome 192 (2001) no. 4, pp. 577-591. http://geodesic.mathdoc.fr/item/SM_2001_192_4_a5/