Property (UWΠ) and localized SVEP

Property (UWΠ) for a bounded linear operator T ∈ L(X) on a Banach space X is a variant of Browder’s theorem, and means that the points λ of the approximate point spectrum for which λI − T is upper semi-Weyl are exactly the spectral points λ such that λI − T is Drazin invertible. In this paper we investigate this property, and we give several characterizations of it by using typical tools from local spectral theory. We also relate this property with some other variants of Browder’s theorem (or Weyl’s theorem)