A note on property (UWΠ)

Let H be a complex infinite dimensional Hilbert space. For T ? B(H), T is said to satisfy property (UW?) if the complement in the approximate point spectrum of the Weyl essential approximate point spectrum coincides with the poles of T. In this paper, we deeply talk about the property (UW?) under some perturbations and property (UW?) for functions of operators. In addition, if T is Drazin invertible, then property (UW?) for functions of T can be transmitted to the functions of its Drazin inverse.