Bulletin of the
Korean Mathematical Society BKMS

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 generalized Weyl's theorem for each function $f$ analytic on some neighborhood of $\sigma(T)$. Also we investigate the stability of generalized Weyl's theorem under (small) compact perturbations.

Keywords: generalized Weyl's theorem, operator approximation, compact perturbations

MSC numbers: Primary 47A10, 47A60; Secondary 47A53, 47A58