Journal of Operator Theory

Volume 68, Issue 2, Fall 2012 pp. 501-514.

Perturbation of semi-Fredholm operators on products of Banach spaces

Authors: Jose Gimenez (1), Manuel Gonzalez (2), and Antonio Martinez-Abejon (3)
Author institution: (1) Departamento de Matematicas, Universidad de los Andes, Merida, 5101, Venezuela
(2) Departamento de Matematicas, Universidad de Cantabria, Santander, E-39071, Spain
(3) Departamento de Matematicas, Universidad de Oviedo, Oviedo, E-33007, Spain

Summary: We show new examples of Banach spaces $X$ and $Y$ for which the component $P\Phi_+(X,Y)$ of the perturbation class for the upper semi-Fredholm operators coincides with the strictly singular operators, or the component $P\Phi_-(X,Y)$ of the perturbation class for the lower semi-Fredholm operators coincides with the strictly cosingular operators. We also show new examples for which the equalities fail.

Keywords: Semi-Fredholm operator, strictly singular, strictly cosingular, perturbation class

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