On the Convergence of Generalized Pseudo-Spectrum

期刊论文
发表日期：

2024年6月1日

查看全文

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

摘要

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.