A Note on *-paranormal Operators

Abstract.

In this note we show that if either T or T^* is totally *-paranormal then Weyl’s theorem holds for f(T) for every f $\in H (\sigma (T))$ , and also a-Weyl’s theorem holds for f(T) if T is totally *-paranormal. We prove that if either T or T^* is *-paranormal then the spectral mapping theorem holds for the Weyl spectrum and for the essential approximate point spectrum.