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