Generalized Weyl’s theorem and spectral continuity for quasi-class (A, k) operators

If T or T* is an algebraically quasi-class (A, k) operator acting on an infinite-dimensional separable Hilbert space, then we prove that generalized Weyl’s theorem holds for f(T) for every f ∈ H(σ(T)), where H(σ(T)) denotes the set of all analytic functions in a neighborhood of σ(T). Moreover, if T* is an algebraically quasi-class (A, k) operator, then generalized a-Weyl’s theorem holds for f(T) for every f ∈ H(σ(T)). Also, we prove that the spectrum, Weyl spectrum and Browder spectrum are continuous on the class of all quasi-class (A, k) operators.