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THE STABILITY OF PROPERTY ($gw$) UNDER COMPACT PERTURBATION
M.H.M. Rashid
,
T. Prasad
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 $\sigma(T)$. Also we investigate the stability of property $(gw)$ under (small) compact perturbations.