Spectral value sets of closed linear operators

We study how the spectrum of a closed linear operator on a complex Banach s pace changes under affine perturbations of the form A curved right arrow A( Delta) = A + D Delta E. Here A, D and E are given linear operators, whereas Delta is an unknown bounded linear operator that parametrizes the possibly unbounded perturbation D Delta E. The union of the spectra of the perturbe d operators A(Delta), with the norm of Delta smaller than a given delta > 0 , is called the spectral value set of A at level delta. In this paper we ex tend a known characterization of these sets for the matrix case to infinite dimensions, and in so doing present a framework that allows for unbounded perturbations of closed linear operators on Banach spaces. The results will be illustrated by applying them to a delay system with uncertain parameter s and to a partial differential equation with a perturbed boundary conditio n.