Weyl’s type theorems for algebraically w-hyponormal operators

Abstract EN

Let T be a bounded linear operator acting on a Hilbert space H.

It is shown that, if T or its adjoint T* is w-hyponormal, then the generalized Weyl theorem holds for ƒ for every ƒ ∈ Hol (σ(T)).

We also show that if T* is w-hyponormal, then the generalized a-Weyl theorem holds for ƒ (T) for every ƒ ∈ Hol (σ (T)) and the B-Weyl spectrum σ BW (T) and the semi-B-Fredholm spectrum σ SBF∓ (T) of T satisfies the spectral mapping theorem.

Finally, we examine the stability of the generalized a-Weyl’s theorem under commutative perturbations by finite rank operators.