Weyl’s Theorem for Algebraically Paranormal Operators

Let T be an algebraically paranormal operator acting on Hilbert space. We prove : (i) Weyl’s theorem holds for f(T) for every f (element of) H((sigma)(T)); (ii) a-Browder’s theorem holds for f(S) for every S (precedes) T and f (element of) H((sigma)(S)); (iii) the spectral mapping theorem holds for the Weyl spectrum of T and for the essential approximate point spectrum of T.