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Weyl's Theorem for Algebraically (π, π)-Quasihyponormal Operators
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Salah Mecheri
Published/Copyright:
March 10, 2010
Abstract
Let π΄ be a bounded linear operator acting on a Hilbert space π». The π΅-Weyl spectrum of π΄ is the set Οπ΅π€(π΄) of all β β β such that π΄ β βπΌ is not a π΅-Fredholm operator of index 0. Let πΈ(π΄) be the set of all isolated eigenvalues of π΄. Recently, in [Berkani and Arroud, J. Aust. Math. Soc. 76: 291β302, 2004] the author showed that if π΄ is hyponormal, then π΄ satisfies the generalized Weyl's theorem Οπ΅π€(π΄) = Ο(π΄) \ πΈ(π΄), and the π΅-Weyl spectrum Οπ΅π€(π΄) of π΄ satisfies the spectral mapping theorem. Lee [Han, Proc. Amer. Math. Soc. 128: 2291β2296, 2000] showed that Weyl's theorem holds for algebraically hyponormal operators. In this paper the above results are generalized to an algebraically (π, π)-quasihyponormal operator which includes an algebraically hyponormal operator.
Key words and phrases:: Hyponormal operator; (π, π)-quasihyponormal operator; Generalized Weyl's theorem; Browder's theorem
Received: 2005-02-11
Revised: 2005-11-08
Published Online: 2010-03-10
Published in Print: 2006-June
Β© Heldermann Verlag
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Keywords for this article
Hyponormal operator;
(π, π)-quasihyponormal operator;
Generalized Weyl's theorem;
Browder's theorem
Articles in the same Issue
- Semimartingale Local Time and the American Put Option
- Existence Theory for Perturbed Nonlinear Boundary Value Problems with Integral Boundary Conditions
- A Generalization of Bihari's Lemma for Discontinuous Functions and Its Application to the Stability Problem of Differential Equations with Impulse Disturbance
- Existence Results for First and Second Order Nonconvex Sweeping Processes with Perturbations and with Delay: Fixed Point Approach
- The Potential Method for the Reactance Wave Diffraction Problem in a Scale of Spaces
- On the Continuity of the Nemytskij Operator between the Spaces πΏπ1(π) and πΏπ2(π)
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- Rate of Approximation for Certain Durrmeyer Operators
- On Decompositions of a Cube into Cubes and Simplexes
- A Positive Answer to Velichko's Question
- An Inverse Result in Simultaneous Approximation by Modified Beta Operators
- Weyl's Theorem for Algebraically (π, π)-Quasihyponormal Operators
- Modulus of Continuity and Best Approximation with Respect to Vilenkin-Like Systems in Some Function Spaces
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