A note on Hausdorff convergence of pseudospectra

• Autorzy: Lindner Marko , Schmeckpeper Dennis

Identyfikatory

DOI

10.7494/OpMath.2023.43.1.101

• Języki publikacji: EN

Abstrakty

EN

For a bounded linear operator on a Banach space, we study approximation of the spectrum and pseudospectra in the Hausdorff distance. We give sufficient and necessary conditions in terms of pointwise convergence of appropriate spectral quantities.

Słowa kluczowe

EN

resolvent; spectrum; pseudospectrum; Hausdorff convergence

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2023
• Tom: Vol. 43, no. 1
• Strony: 101--108
• Opis fizyczny: Bibliogr. 14 poz.

Twórcy

autor

Lindner Marko

• TU Hamburg, Institute of Mathematics, Am Schwarzenberg - Campus 1, 21073 Hamburg, Germany

autor

Schmeckpeper Dennis

• TU Hamburg, Institute of Mathematics, Am Schwarzenberg - Campus 1, 21073 Hamburg, Germany

Bibliografia

• [1] S.N. Chandler-Wilde, R. Chonchaiya, M. Lindner, On spectral inclusion sets and computing the spectra and pseudospectra of bounded linear operators, in preparation.
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• [3] E.B. Davies, E. Shargorodsky, Level sets of the resolvent norm of a linear operator revisited, Mathematika 62 (2015), no. 1, 243–265.
• [4] M.M. Day, Some more uniformly convex spaces, Bull. Amer. Math. Soc. 47 (1941), 504–507.
• [5] F. Gabel, D. Gallaun, J. Grossmann, M. Lindner, R. Ukena, Spectral approximation of generalized Schrödinger operators via approximation of subwords, in preparation.
• [6] J. Globevnik, Norm-constant analytic functions and equivalent norms, Illinois J. Math. 20 (1976), no. 3, 503–506.
• [7] R. Hagen, S. Roch, B. Silbermann, C∗-Algebras and Numerical Analysis, Monographs and Textbooks in Pure and Applied Mathematics, vol. 236, Marcel Dekker, Inc., New York, Basel, 2001.
• [8] R. Hagger, M. Lindner, M. Seidel, Essential pseudospectra and essential norms of band-dominated operators, J. Math. Anal. Appl. 437 (2016), no. 1, 255–291.
• [9] M. Lindner, D. Schmeckpeper, How stability indicators determine asymptotics of resolvents, condition numbers and pseudospectra, in preparation.
• [10] M. Lindner, M. Seidel, An affirmative answer to a core issue on limit operators, J. Funct. Anal. 267 (2014), no. 3, 901–917.
• [11] E. Shargorodsky, On the level sets of the resolvent norm of a linear operator, Bull. London Math. Soc. 40 (2008), no. 3, 493–504.
• [12] E. Shargorodsky, On the definition of pseudospectra, Bull. London Math. Soc. 41 (2009), no. 3, 524–534.
• [13] E. Shargorodsky, S. Shkarin, The level sets of the resolvent norm and convexity properties of Banach spaces, Arch. Math. 93 (2009), no. 1, 59–66.
• [14] L.N. Trefethen, M. Embree, Spectra and Pseudospectra: The Behavior of Nonnormal Matrices and Operators, Princeton Univ. Press, Princeton, NJ, 2005.

Uwagi

Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023)