Generalized weyl's theorem for algebraically quasi-paranormal operators
Department Of Mathematics, College Of Sciences, Kyung Hee University, Seoul 130-701, Republic Of Korea
Journal of Inequalities and Applications 2012, 2012:89 doi:10.1186/1029-242X-2012-89Published: 17 April 2012
Let T or T* be an algebraically quasi-paranormal operator acting on a Hilbert space. We prove: (i) generalized Weyl's theorem holds for f(T) for every f ∈ H(σ (T)); (ii) generalized a-Browder's theorem holds for f(S) for every S ≺ T and f ∈ H(σ(S)); (iii) the spectral mapping theorem holds for the B-Weyl spectrum of T. Moreover, we show that if T is an algebraically quasi-paranormal operator, then T + F satisfies generalized Weyl's theorem for every algebraic operator F which commutes with T.
Mathematics Subject Classification (2010): Primary 47A10, 47A53; Secondary 47B20.