A note on generalized Weyl’s theorem

We prove that if either T or T ∗ has the single-valued extension property, then the spectral mapping theorem holds for B-Weyl spectrum. If, moreover T is isoloid, and generalizedWeyl’s theorem holds for T , then generalized Weyl’s theorem holds for f (T ) for every f ∈ H(σ (T )). An application is given for algebraically paranormal operators.  2005 Elsevier Inc. All rights reserved.