New approach to property (ω) for functions of operators

Abstract

Let H be an infinite dimensional complex Hilbert space and B(H) be the algebra of all bounded linear operators on H. For T ∈ B(H), we say T satisfies property (ω) if _σa(T) \ σea(T) = _π00(T), where _π00(T) = {λ ∈ _isoσ(T) : 0 < n(T − λI) < ∞}. In this paper, we research on the property (ω) for functions of operators by using the new spectrum σvea(T) which is a variant of the Weyl essential approximate point spectrum. At the same time, the stability of SVEP  as well as the relationships between the two parts is also given.