On the distribution of the discrete spectrum of nuclearly perturbed operators in Banach spaces

Abstract

Let Z_0 be a bounded operator in a Banach space X with purely essential spectrum and K a nuclear operator in X. Using methods of complex analysis we study the discrete spectrum of Z_0+K and derive a Lieb-Thirring type inequality. We obtain estimates for the number of eigenvalues in certain regions of the complex plane and an estimate for the asymptotics of the eigenvalues approaching to the essential spectrum of Z_0

References in corpus (2)

• Variation of discrete spectra for non-selfadjoint perturbations of selfadjoint operators
• Blaschke-type conditions in unbounded domains, generalized convexity and applications in perturbation theory