A Note on a-Weyl’s Theorem

If T or T* is log-hyponormal then for every f HŽ ŽT.., Weyl’s theorem holds for fŽT., where HŽ ŽT.. denotes the set of all analytic functions on an open neighborhood of ŽT.. Moreover, if T* is p-hyponormal or log-hyponormal or M-hyponormal then for every f HŽ ŽT.., a-Weyl’s theorem holds for fŽT.. Also it is shown that if we let A T BŽH.: T* is log-hyponormal4then the approximate point spectrum, the essential approximate point spectrum, and the Browder essential approximate point spectrum are continuous in A.