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2023•Journal of Spectral TheoryOpen access

Generalised norm resolvent convergence: comparison of different concepts

Olaf Post, Sebastian Zimmer

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Abstract

In this paper, we show that the two concepts of generalised norm resolvent convergence introduced by Weidmann and the first named 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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What this paper is about

In this paper, we show that the two concepts of generalised norm resolvent convergence introduced by Weidmann and the first named 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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OpenAlex reports 3 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

In this paper, we show that the two concepts of generalised norm resolvent convergence introduced by Weidmann and the first named 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.

Key concepts: Resolvent, Convergence (economics), Norm (philosophy), Applied mathematics, Mathematics, Focus (optics), Normal convergence, Computer science

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