Criteria of completeness of generalized eigenvectors of a class of compact or compact-resolvent non-self-adjoint operators and applications

In this work we establish sufficient conditions on the denseness of the generalized eigenvectors for a class of compact (or compact resolvent) non self adjoint operators. We can apply our results to operators arising in many fields, particularly in field's theory and in abstract second order differential equations. Our results generalize some results of Aimar and al [1] and [2], Macaev and Keldysh [11] and Dunford-Schwartz [9].