Generalised norm resolvent convergence: comparison of different concepts

2022/02/07 by Olaf Post, Sebastian Zimmer, Post, Olaf +1 · 3 citations
Computer Science · Engineering · Mathematics · #47A55 #47B02 #FOS: Mathematics #Functional Analysis (math.FA) #Matrix Theory and Algorithms #Numerical Analysis (math.NA) #Numerical methods in inverse problems #Spectral Theory (math.SP) #Stability and Control of Uncertain Systems

paper · pdf · doi:10.48550/arxiv.2202.03234

openalex publication_date 2022/02/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we show that the two concepts of generalised norm resolvent convergence introduced by Weidmann and the first author of this paper are equivalent. We also focus on the convergence speed and provide conditions under which the convergence speed is the same for both concepts. We illustrate the abstract results by a large number of examples.

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