Georgian Mathematical Journal 13 (2006), No. 2, 307--313
Copyright Heldermann Verlag 2006
Weyl's Theorem for Algebraically (p,k)-Quasihyponormal Operators
Salah Mecheri
Dept. of Mathematics, King Saud University, College of Science, P. O. Box 2455, Riyadh 11451, Saudi Arabia
mecherisalah@hotmail.com
[Abstract-pdf]
Let $A$ be a bounded linear operator acting on a Hilbert space $H$. The $B$-Weyl spectrum of $A$ is the set $\sigma_{Bw}(A)$ of all $\lambda \in\mathbb C$ such that $A-\lambda I$ is not a $B$-Fredholm operator of index 0. Let $E(A)$ be the set of all isolated eigenvalues of $A$. Recently M. Berkani and A. Arroud [J. Aust. Math. Soc. 76 (2004) 291--302] showed that if $A$ is hyponormal, then $A$ satisfies the generalized Weyl's theorem $\sigma_{Bw}(A) = \sigma(A)\setminus E(A)$, and the $B$-Weyl spectrum $\sigma_{Bw}(A)$ of $A$ satisfies the spectral mapping theorem. Y. M. Han and W. Y. Lee [Proc. Amer. Math. Soc. 128 (2000) 2291--2296] showed that Weyl's theorem holds for algebraically hyponormal operators. In this paper the above results are generalized to an algebraically ($p,k$)-quasihyponormal operator which includes an algebraically hyponormal operator.
Keywords: Hyponormal operator, (p,k)-quasihyponormal operator, Generalized Weyl's theorem, Browder's theorem.
MSC: 47A10, 47A12, 47B20
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