GENERALIZED WEYL'S THEOREM FOR POSINORMAL OPERATORS

2007 ◽  
Vol 107A (1) ◽  
pp. 81-89
Author(s):  
S. Mecheri
Keyword(s):  
Weyl’S Theorem ◽  
Generalized Weyl’S Theorem

GENERALIZED WEYL'S THEOREM FOR ALGEBRAICALLY $k$-QUASI-PARANORMAL OPERATORS

2012 ◽  
Vol 25 (4) ◽  
pp. 655-668 ◽  
Author(s):  
D. Senthilkumar ◽  
P. Maheswari Naik ◽  
N. Sivakumar
Keyword(s):  
Weyl’S Theorem ◽  
Generalized Weyl’S Theorem

On Quasi-Class A Operators

2013 ◽  
Vol 59 (1) ◽  
pp. 163-172
Author(s):  
Salah Mecheri
Keyword(s):  
Hilbert Space ◽  
Analytic Function ◽  
Complex Hilbert Space ◽  
Linear Operators ◽  
Weyl’S Theorem ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
Infinite Dimensional ◽  
Class A ◽  
Generalized Weyl’S Theorem

Abstract Let H be a separable infinite dimensional complex Hilbert space, and let B(H) denote the algebra of all bounded linear operators on H. Let A;B be operators in B(H). In this paper we prove that if A is quasi-class A and B* is invertible quasi-class A and AX = XB, for some X ∈ C2 (the class of Hilbert-Schmidt operators on H), then A*X = XB*. We also prove that if A is a quasi-class A operator and f is an analytic function on a neighborhood of the spectrum of A, then f(A) satisfies generalized Weyl's theorem. Other related results are also given.

scholarly journals Generalized Weyl’s theorems for polaroid operators

2011 ◽  
Vol 27 (1) ◽  
pp. 24-33
Author(s):  
C. CARPINTERO ◽  
◽  
D. MUNOZ ◽  
E. ROSAS ◽  
O. GARCIA ◽  
...  
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Linear Operators ◽  
Weyl’S Theorem ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
Generalized Weyl’S Theorem ◽  
Polaroid Operators ◽  
Weyl Theorem ◽  
Necessary And Sufficient

In this paper we establish necessary and sufficient conditions on bounded linear operators for which generalized Weyl’s theorem, or generalized a-Weyl theorem, holds. We also consider generalized Weyl’s theorems in the framework of polaroid operators and obtain improvements of some results recently established in [20] and [29].

scholarly journals Generalized Weyl's theorem and hyponormal operators

2004 ◽  
Vol 76 (2) ◽  
pp. 291-302 ◽  
Author(s):  
M. Berkani ◽  
A. Arroud
Keyword(s):  
Hilbert Space ◽  
Weyl’S Theorem ◽  
Hyponormal Operator ◽  
Spectral Mapping Theorem ◽  
Spectral Mapping ◽  
Bounded Linear ◽  
Generalized Weyl’S Theorem ◽  
Weyl Spectrum ◽  
Hyponormal Operators ◽  
Isolated Eigenvalues

AbstractLet T be a bounded linear operator acting on a Hilbert space H. The B-Weyl spectrum of T is the set σBW(T) of all λ ∈ Сsuch that T − λI is not a B-Fredholm operator of index 0. Let E(T) be the set of all isolated eigenvalues of T. The aim of this paper is to show that if T is a hyponormal operator, then T satisfies generalized Weyl's theorem σBW(T) = σ(T)/E(T), and the B-Weyl spectrum σBW(T) of T satisfies the spectral mapping theorem. We also consider commuting finite rank perturbations of operators satisfying generalized Weyl's theorem.

Sign in / Sign up

Export Citation Format

Share Document