On extended eigenvalues and extended eigenvectors of truncated shift

Hasan Alkanjo

Concrete Operators (2013)

  • Volume: 1, page 19-27
  • ISSN: 2299-3282

Abstract

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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..

How to cite

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Hasan Alkanjo. "On extended eigenvalues and extended eigenvectors of truncated shift." Concrete Operators 1 (2013): 19-27. <http://eudml.org/doc/266777>.

@article{HasanAlkanjo2013,
abstract = {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..},
author = {Hasan Alkanjo},
journal = {Concrete Operators},
keywords = {Extended eigenvalues; extended eigenvectors; Blaschke product; model space; extended eigenvalues},
language = {eng},
pages = {19-27},
title = {On extended eigenvalues and extended eigenvectors of truncated shift},
url = {http://eudml.org/doc/266777},
volume = {1},
year = {2013},
}

TY - JOUR
AU - Hasan Alkanjo
TI - On extended eigenvalues and extended eigenvectors of truncated shift
JO - Concrete Operators
PY - 2013
VL - 1
SP - 19
EP - 27
AB - 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..
LA - eng
KW - Extended eigenvalues; extended eigenvectors; Blaschke product; model space; extended eigenvalues
UR - http://eudml.org/doc/266777
ER -

References

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  1. [1] H. Bercovici. Operator theory and arithmetic in H1, volume 26 of Mathematical Surveys and Monographs. American Mathematical Society, Providence, RI, 1988. 
  2. [2] A. Biswas and S. Petrovic. On extended eigenvalues of operators. Integral Equations Operator Theory, 55(2):233–248, 2006. Zbl1119.47019
  3. [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. [4] M. Rosenblum. On the operator equation BX − XA = Q. Duke Math. J., 23:263–269, 1956. 
  5. [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. Zbl1183.30031
  6. [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. Zbl0201.45003

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