Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 36, 2011, 481-491
Universidad de Cantabria, Facultad de Ciencias, Departamento de Matemáticas
E-39071 Santander, España; gonzalem 'at' unican.es
Universidad de Oviedo, Facultad de Ciencias, Departamento de Matemáticas
E-33007 Oviedo, España; ama 'at' uniovi.es
Universidad de Oriente, Departamento de Matemáticas
6101 Cumaná, Venezuela; msalas@sucre.udo.edu.ve
Abstract. We prove that the component P\Phi+(X,Y) of the perturbation class for the upper semi-Fredholm operators between Banach spaces X and Y coincide with the strictly singular operators when every closed infinite dimensional subspace of X contains an infinite dimensional complemented subspace whose complement is isomorphic to X. Similarly, we prove that the component P\Phi-(X,Y) of the perturbation class for the lower semi-Fredholm operators coincide with the strictly cosingular operators when every infinite codimensional subspace of Y is contained in an infinite codimensional complemented subspace isomorphic to Y. We also give examples of Banach spaces satisfying the aforementioned conditions.
2010 Mathematics Subject Classification: Primary 47A53, 47A55.
Key words: Perturbation class, semi-Fredholm operator, strictly singular operator, strictly cosingular operator, subprojective space, superprojective space.
Reference to this article: M. González, A. Martínez-Abejón and M. Salas-Brown: Perturbation classes for semi-Fredholm operators on subprojective and superprojective spaces. Ann. Acad. Sci. Fenn. Math. 36 (2011), 481-491.
doi:10.5186/aasfm.2011.3625
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