On extended eigenvalues and extended eigenvectors of truncated shift

• Autorzy: Hasan Alkanjo
• Języki publikacji: EN

Abstrakty

EN

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..

Słowa kluczowe

EN

Extended eigenvalues; extended eigenvectors; Blaschke product; model space

• Wydawca: De Gruyter Open
• Czasopismo: Concrete Operators
• Rocznik: 2013
• Tom: 1
• Strony: 19-27

Daty

otrzymano

2013-02-20

zaakceptowano

2013-07-18

online

2013-07-29

Twórcy

autor

Hasan Alkanjo

• Université de Lyon; Université Lyon 1; Institut Camille Jordan CNRS UMR 5208; 43, boulevard du 11 Novembre 1918, F-69622 Villeurbanne

Bibliografia

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

Identyfikatory

DOI

10.2478/conop-2012-0003