WEYL TYPE THEOREMS FOR FUNCTIONS OF OPERATORS

Abstract

Abstract A-Weyl's theorem and property (ω), as two variations of Weyl's theorem, were introduced by Rakočević. In this paper, we study a-Weyl's theorem and property (ω) for functions of bounded linear operators. A necessary and sufficient condition is given for an operator T to satisfy that f ( T ) obeys a-Weyl's theorem (property (ω)) for all f ∈ Hol(σ( T )). Also we investigate the small-compact perturbations of operators satisfying a-Weyl's theorem (property (ω)) in the setting of separable Hilbert spaces.