Topological uniform descent and compact perturbations

Abstract

Let $$\mathcal {H}$$ be an infinite dimensional separable complex Hilbert space and $$\mathcal {B(H)}$$ the algebra of all bounded linear operators on $$\mathcal {H}$$ . In this paper, we characterize some features of the topological uniform descent resolvent set $$\rho _\tau (T)$$ for an operator $$T\in \mathcal {B(H)}$$ , and give a classification of the components of $$\rho _\tau (T)$$ . Then using topological uniform descent spectrum and $$\rho _\tau (T)$$ , we discuss the SVEP and further characterize those operators for which the SVEP is preserved under compact perturbations.