The stability of property (gw) under compact perturbation
M. H. M. Rashid, T. Prasad



Let H be a complex separable infinite dimensional Hilbert space. In this paper, a necessary and sufficient condition is given for an operator T on H to satisfy that f(T) obeys property (g w) for each function f analytic on some neighborhood of σ(T). Also, we investigate the stability of property (g w) under (small) compact perturbations.