Weyl's Theorem for Algebraically Totally K - Quasi - Paranormal Operators

An operator ) (H B T  is said to be k quasi paranormal operator if x T x T x T k k k 2 2 1    for every H x , k is a natural number. This class of operators contains the class of paranormal operators and the class of quasi class A operators. Let T or T be an algebraically k quasi paranormal operator acting on Hilbert space. Using Local Spectral Theory, we prove (i)Weyl's theorem holds for f(T) for every )) ( ( T H f   ; (ii) a-Browder's theorem holds for f (S) for every T S  and )) ( ( S H f   ; (iii) the spectral mapping theorem holds for the Weyl spectrum of T and for the essential approximate point spectrum of T.