Opuscula Math. 41, no. 3 (2021), 395-412
https://doi.org/10.7494/OpMath.2021.41.3.395

Opuscula Mathematica

# Spectrum localization of a perturbed operator in a strip and applications

Michael Gil'

Abstract. Let $$A$$ and $$\tilde{A}$$ be bounded operators in a Hilbert space. We consider the following problem: let the spectrum of $$A$$ lie in some strip. In what strip the spectrum of $$\tilde{A}$$ lies if $$A$$ and $$\tilde{A}$$ are "close"? Applications of the obtained results to integral operators and matrices are also discussed. In addition, we apply our perturbation results to approximate the spectral strip of a Hilbert-Schmidt operator by the spectral strips of finite matrices.

Keywords: operator, spectrum, perturbation, approximation, integral operator, matrix.

Mathematics Subject Classification: 47A10, 47A55, 47B10.

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• Communicated by P.A. Cojuhari.
• Received: 2020-12-24.
• Accepted: 2021-01-24.
• Published online: 2021-04-19.

Cite this article as:
Michael Gil', Spectrum localization of a perturbed operator in a strip and applications, Opuscula Math. 41, no. 3 (2021), 395-412, https://doi.org/10.7494/OpMath.2021.41.3.395

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