On the Asymptotic Behavior of the Eigenvalues of an Analytic Operator in the Sense of Kato

Aref Jeribi ()
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Aref Jeribi: University of Sfax, Department of Mathematics

Chapter Chapter 11 in Perturbation Theory for Linear Operators, 2021, pp 361-388 from Springer

Abstract: Abstract The basic idea of this chapter is to derive a precise description, on a separable Hilbert space X, to the behavior of the spectrum of a self-adjoint operator $$T_0$$ T 0 after a perturbation by an infinite sum of operators where $$\varepsilon \in \mathbb {C}$$ ε ∈ C and $$T_1$$ T 1 , $$T_2$$ T 2 , $$T_3\ldots $$ T 3 … are linear operators on the space X having the same domain $$\mathcal{D}\supset \mathcal{D}(T_0)$$ D ⊃ D ( T 0 ) and satisfying a specific growing inequality, while the spectrum of $$T_0$$ T 0 is discrete and its eigenvalues are not condensed.

Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-981-16-2528-2_11

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DOI: 10.1007/978-981-16-2528-2_11

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