SVEP and compact perturbations

Let H be a complex separable infinite dimensional Hilbert space. In this paper, we prove that an operator T acting on H is a norm limit of those operators with single-valued extension property (SVEP for short) if and only if T ⁎ , the adjoint of T, is quasitriangular. Moreover, if T ⁎ is quasitriangular, then, given an ε > 0 , there exists a compact operator K on H with ‖ K ‖ < ε such that T + K has SVEP. Also, we investigate the stability of SVEP under (small) compact perturbations. We characterize those operators for which SVEP is stable under (small) compact perturbations.