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Weyl's Theorem for Algebraically (𝑝, 𝑘)-Quasihyponormal Operators
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Salah Mecheri
Veröffentlicht/Copyright:
10. März 2010
Abstract
Let 𝐴 be a bounded linear operator acting on a Hilbert space 𝐻. The 𝐵-Weyl spectrum of 𝐴 is the set σ𝐵𝑤(𝐴) of all ⋋ ∈ 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 [Berkani and Arroud, J. Aust. Math. Soc. 76: 291–302, 2004] the author showed that if 𝐴 is hyponormal, then 𝐴 satisfies the generalized Weyl's theorem σ𝐵𝑤(𝐴) = σ(𝐴) \ 𝐸(𝐴), and the 𝐵-Weyl spectrum σ𝐵𝑤(𝐴) of 𝐴 satisfies the spectral mapping theorem. Lee [Han, Proc. Amer. Math. Soc. 128: 2291–2296, 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.
Key words and phrases:: Hyponormal operator; (𝑝, 𝑘)-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
© Heldermann Verlag
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Schlagwörter für diesen Artikel
Hyponormal operator;
(𝑝, 𝑘)-quasihyponormal operator;
Generalized Weyl's theorem;
Browder's theorem
Artikel in diesem Heft
- 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 𝐿𝑝1(𝑋) and 𝐿𝑝2(𝑋)
- Monadic 𝐵𝐿-Algebras
- 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 (𝑝, 𝑘)-Quasihyponormal Operators
- Modulus of Continuity and Best Approximation with Respect to Vilenkin-Like Systems in Some Function Spaces
- Exact Distributions of the Product and Ratio of Absolute Values of Pearson Type VII and Bessel Function Random Variables
- An Automatically Stable and Order Three Split Rational Approximation of a Semigroup
- Selfadjoint Operators and Generalized Central Algorithms in Frechet Spaces
- Oscillation Theorems for Certain Even Order Delay Differential Equations Involving General Means
- Corrections to “On a Singular Direction of a Meromorphic Function”
