Salah Mecheri

Weyl's Theorem for Algebraically (p,k)-Quasihyponormal Operators

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 $A$. In 2004 M. Berkani and A. Arroud 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. Lee in 2000 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.

Hyponormal operator, $(p,k)$-quasihyponormal operator, Generalized Weyl's theorem, Browder's theorem.

MSC 2000: 47A10, 47A12, 47B20