Weyl’s theorem for algebrascally wF(p, r, q) operators with p, q > 0 and q ≥ 1 - Rashid, M. H. M. (Ukrains’kyi Matematychnyi Zhurnal, 2011)
If T or T* is an algebraically wF(p, r, q) operator with p, r > 0 and q ≥ 1 acting on an infinite-dimensional separable Hilbert space, then we prove that the Weyl theorem holds for f(T), for every f Hol(σ(T)), where Hol(σ(T)) denotes the set of all analytic functions in an open neighborhood of σ(T). Moreover, if T^* is a wF(p, r, q) operator with p, r > 0 and q ≥ 1, then the a-Weyl theorem holds for f(T). Also, if T or T^* is an algebraically wF(p, r, q) operators with p, r > 0 and q ≥ 1, then we establish spectral mapping theorems for the Weyl spectrum and essential approximate point spectrum of T for every f Hol(σ(T)), respectively. Finally, we examine the stability of the Weyl theorem and a-Weyl theorem under commutative perturbation by finite-rank operators.