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Title: Generalized weyl’s theorem for some classes of operators
Authors: Mecheri, Salah
Keywords: Generalized Weyl’s Theorem
Hyponormal operators
Toeplitz operators
B-Fredholm operator
B-Weyl 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; 553-563
Abstract: Let A be a bounded linear operator acting on a Hilbert space H. The B-Weyl spectrum of A is the set ¾Bw(A) of all ¸ 2 C such that A¡¸I is not a B-Fredholm 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 B-Weyl 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 semi-normal 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 p-hyponormal 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: 1225-6951
Appears in Collections:College of Science

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