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Concrete Operators

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On extended eigenvalues and extended eigenvectors of truncated shift

Hasan Alkanjo
  • Université de Lyon; Université Lyon 1; Institut Camille Jordan CNRS UMR 5208; 43, boulevard du 11 Novembre 1918, F-69622 Villeurbanne
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Published Online: 2013-07-29 | DOI: https://doi.org/10.2478/conop-2012-0003


In this paper we consider the truncated shift operator Su on the model space K2u := H2 θ uH2. We say that a complex number λ is an extended eigenvalue of Su if there exists a nonzero operator X, called extended eigenvector associated to λ, and satisfying the equation SuX = λXSu. We give a complete description of the set of extended eigenvectors of Su, in the case of u is a Blaschke product..

Keywords: Extended eigenvalues; extended eigenvectors; Blaschke product; model space

  • [1] H. Bercovici. Operator theory and arithmetic in H1, volume 26 of Mathematical Surveys and Monographs. American Mathematical Society, Providence, RI, 1988. Google Scholar

  • [2] A. Biswas and S. Petrovic. On extended eigenvalues of operators. Integral Equations Operator Theory, 55(2):233–248, 2006. Google Scholar

  • [3] N. K. Nikol0ski˘ı. Treatise on the shift operator, volume 273 of Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences]. Springer-Verlag, Berlin, 1986. Spectral function theory, With an appendix by S. V. Hrušcev [S. V. Khrushchëv] and V. V. Peller, Translated from the Russian by Jaak Peetre. Google Scholar

  • [4] M. Rosenblum. On the operator equation BX − XA = Q. Duke Math. J., 23:263–269, 1956. Google Scholar

  • [5] D. Sarason. Free interpolation in the Nevanlinna class. In Linear and complex analysis, volume 226 of Amer. Math. Soc. Transl. Ser. 2, pages 145–152. Amer. Math. Soc., Providence, RI, 2009. Google Scholar

  • [6] B. Sz.-Nagy and C. Foias. Harmonic analysis of operators on Hilbert space. Translated from the French and revised. North-Holland Publishing Co., Amsterdam, 1970.Google Scholar

About the article

Received: 2013-02-20

Accepted: 2013-07-18

Published Online: 2013-07-29

Citation Information: Concrete Operators, Volume 1, Pages 19–27, ISSN (Online) 2299-3282, DOI: https://doi.org/10.2478/conop-2012-0003.

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©2013 Versita Sp. z o.o.. This content is open access.

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