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

الأصل · EN

Let Z₀ 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 Z₀+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 Z₀