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Finite Section Method in a Space with Two Norms

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Abstract

We compare the finite central truncations of a given matrix with respect to two non-equivalent Hilbert space norms. While the limit sets of the finite sections spectra are merely located via numerical range bounds, the weak \(*\)-limits of the counting measures of these spectra are proven in general to be gravi-equivalent with respect to the logarithmic potential in the complex plane. Classical methods of factorization of Volterra type or Wiener–Hopf type operators lead to a series of effective criteria of asymptotic equivalence, or uniform boundedness of the two sequences of truncations. Examples from function theory, integral equations and potential theory complement the theoretical results.

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Authors and Affiliations

  1. Department of Mathematics, University of California at Santa Barbara, Santa Barbara, CA, 93106, USA

    Mihai Putinar

  2. School of Mathematics, Statistics and Physics, Newcastle University, Newcastle upon Tyne, NE1 7RU, UK

    Mihai Putinar

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  1. Mihai Putinar
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Correspondence to Mihai Putinar.

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Don Sarason, in memoriam.

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Putinar, M. Finite Section Method in a Space with Two Norms. Integr. Equ. Oper. Theory 89, 345–376 (2017). https://doi.org/10.1007/s00020-017-2404-8

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  • DOI: https://doi.org/10.1007/s00020-017-2404-8

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