A characterization of unbounded generalized meromorphic operators

Abstract

In this paper, we study the class of unbounded generalized meromorphic operators GM(E, ∞), where E is a finite subset of C, which generalizes the notion of unbounded meromorphic operators. More precisely, we give a decomposition and some characterizing properties of these operators based on the punctured neighborhood theorem and the operational calculus for unbounded operators.

Stability of some essential B-spectra of pencil operators and application

“…Proof. If M = I, then we obtain the result established in [7]. If M = I, then the fact that T is a semi B-Fredholm operator, this implies from Proposition 2.1, the existence of two T-invariant closed subspaces X 0 and X 1 such that…”