A new criteria for two Weyl’s type theorems

Let B(H) be the collection of all bounded linear operators on H, where H is an infinite dimensional complex Hilbert space. For T ? B(H), we say property (UW?)( property (?)) holds for T if ?a(T)\?ea(T) = ?(T)(?00(T)), where ?a(T) and ?ea(T) denote the approximate point spectrumand the essential approximate point spectrum of T, respectively, also ?(T) and ?00(T) severally denote the set of all poles and all finite dimensional isolated eigenvalues. In this note, we introduce a new judgement method for bounded linear operators and their function calculus satisfying property (UW?) and property (?) together by the deformed property. Meanwhile, we investigate the relationships among property (UW?), property (?) and hypercyclic property.