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The stability of property ( $g w$ ) under compact perturbation

$icon-email$ M.H.M. Rashid , T. Prasad

Abstract

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.

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The stability of property (gw) under compact perturbation

Abstract

The stability of property ( $g w$ ) under compact perturbation