On a Riesz basis of finite-dimensional invariant subspaces and application to Gribov operator in Bargmann space

摘要

In this paper, we are mainly concerned with a new class of unbounded perturbations of unbounded normal operators. We give a description of the changed spectrum and we establish different conditions in terms of the spectrum to prove the existence of Riesz basis of finite-dimensional invariant subspaces of generalized eigenvectors. The obtained results are of importance for application to a non-self-adjoint Gribov operator in Bargmann space.