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Title:  Generalized weyl’s theorem for some classes of operators 
Authors:  Mecheri, Salah 
Keywords:  Generalized Weyl’s Theorem Classes Hyponormal operators Toeplitz operators BFredholm operator BWeyl spectrum Hermitian operators Linear operator (p,k)quasihyponormal operator Paranormal operator Browder’s theorem 
Issue Date:  2006 
Publisher:  Kyungpook National University 
Citation:  Kyungpook Mathematical Journal: 46; 553563 
Abstract:  Let A be a bounded linear operator acting on a Hilbert space H. The BWeyl
spectrum of A is the set ¾Bw(A) of all ¸ 2 C such that A¡¸I is not a BFredholm operator
of index 0. Let E(A) be the set of all isolated eigenvalues of A. Recently in [6] Berkani
showed that if A is a hyponormal operator, then A satisfies generalized Weyl’s theorem
¾Bw(A) = ¾(A) n E(A), and the BWeyl spectrum ¾Bw(A) of A satisfies the spectral
mapping theorem. In [51], H. Weyl proved that weyl’s theorem holds for hermitian operators.
Weyl’s theorem has been extended from hermitian operators to hyponormal and
Toeplitz operators [12], and to several classes of operators including seminormal operators
([9], [10]). Recently W. Y. Lee [35] showed that Weyl’s theorem holds for algebraically
hyponormal operators. R. Curto and Y. M. Han [14] have extended Lee’s results to algebraically
paranormal operators. In [19] the authors showed that Weyl’s theorem holds
for algebraically phyponormal operators. As Berkani has shown in [5], if the generalized
Weyl’s theorem holds for A, then so does Weyl’s theorem. In this paper all the above results
are generalized by proving that generalizedWeyl’s theorem holds for the case where A
is an algebraically (p; k)quasihyponormal or an algebarically paranormal operator which
includes all the above mentioned operators. 
Description:  Department of Mathematics, King Saud University, College of Science, P. O. Box
2455, Riyadh 11451, Saudi Arabia
email : mecherisalah@hotmail.com 
URI:  http://hdl.handle.net/123456789/2690 
ISSN:  12256951 
Appears in Collections:  College of Science

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