On the hereditary character of certain spectral properties and some applications





Weyl type theorems, Restrictions of operators, Integral operators, Spectral properties, semi-Fredholm theory


In this paper we study the behavior of certain spectral properties of an operator T on a proper closed and T-invariant subspace W ⊆ X such that Tn (X) ⊆ W, for some n ≥ 1, where T ∈ L(X) and X is an infinite-dimensional complex Banach space. We prove that for these subspaces a large number of spectral properties are transmitted from T to its restriction on W and vice-versa. As consequence of our results, we give conditions for which semiFredholm spectral properties, as well as Weyl type theorems, are equivalent for two given operators. Additionally, we give conditions under which an operator acting on a subspace can be extended on the entire space preserving the Weyl type theorems. In particular, we give some applications of these results for integral operators acting on certain functions spaces.


Author Biographies

Carlos Rafael Carpintero, Corporación Universitaria del Caribe-CECAR.

Facultad de Cs. Básicas, Ingen. y Arquitectura.

Ennis Rafael Rosas Rodriguez, Universidad de la Costa.

Dept. de Ciencias Naturales y Exactas.

Orlando J. García Mojica, Corporación Universitaria del Caribe-CECAR.

Facultad de Cs. Básicas, Ingen. y Arquitectura

José Eduardo Sanabria, Universidad de Sucre.

Dept. de Matemáticas.

Andrés Malaver, Universidad de Oriente.

Dept. de Matemáticas.


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2021-04-19 — Updated on 2021-08-04

How to Cite

C. R. Carpintero, E. R. Rosas Rodriguez, O. J. García Mojica, J. E. Sanabria, and A. . Malaver, “On the hereditary character of certain spectral properties and some applications”, Proyecciones (Antofagasta, On line), vol. 40, no. 5, pp. 1053-1069, Aug. 2021.