Hilbert空间中线性算子s -伪谱的表征

IF 0.8 4区数学 Q2 MATHEMATICS

Filomat Pub Date : 2023-01-01 DOI:10.2298/fil2305331a

A. Ammar, Ameni Bouchekoua, A. Jeribi

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引用次数: 0

摘要

本文引入并研究了Hilbert空间中由非严格不等式定义的线性算子的s伪谱。灵感来自a ? B?在s的结果[3]中，证明了有界线性算子的s -可解范数在s -可解集的任何开集中都不是常数。此外，我们利用具有严格小于?范数的扰动的所有扰动算子的s谱，得到了有界线性算子的s伪谱的一个表征。

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A characterization of S-pseudospectra of linear operators in a Hilbert space

In this work, we introduce and study the S-pseudospectra of linear operators defined by nonstrict inequality in a Hilbert space. Inspired by A. B?ttcher?s result [3], we prove that the S-resolvent norm of bounded linear operators is not constant in any open set of the S-resolvent set. Beside, we find a characterization of the S-pseudospectrum of bounded linear operator by means the S-spectra of all perturbed operators with perturbations that have norms strictly less than ?.

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