On the Convergence of Generalized Pseudo-Spectrum

IF 0.6 4区数学 Q3 MATHEMATICS

Mathematical Notes Pub Date : 2024-07-15 DOI:10.1134/s0001434624050316

M. A. Mansouri, A. Khellaf, H. Guebbai

引用次数: 0

Abstract

In this paper, we study the convergence of generalized pseudo-spectrum associated with bounded operators in a Hilbert space. We prove that the approximate generalized pseudo-spectrum converges to the exact set under norm convergence. To prove this result, we use the Hausdorff distance and the assumption that the generalized resolvent operator is not constant on any open subset of the generalized resolvent set.

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论广义伪谱的收敛性

摘要本文研究了希尔伯特空间中与有界算子相关的广义伪谱的收敛性。我们证明，在规范收敛条件下，近似广义伪谱收敛于精确集。为了证明这一结果，我们使用了 Hausdorff 距离，并假设广义解析算子在广义解析集的任何开放子集上都不是常数。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Mathematical Notes 数学-数学

CiteScore

0.90

自引率

16.70%

发文量

179

审稿时长

24 months

期刊介绍： Mathematical Notes is a journal that publishes research papers and review articles in modern algebra, geometry and number theory, functional analysis, logic, set and measure theory, topology, probability and stochastics, differential and noncommutative geometry, operator and group theory, asymptotic and approximation methods, mathematical finance, linear and nonlinear equations, ergodic and spectral theory, operator algebras, and other related theoretical fields. It also presents rigorous results in mathematical physics.