Stabilité du spectre ponctuel d'opérateurs de Toeplitz généralisés

Lioudmila Nikolskaia

Studia Mathematica (1995)

  • Volume: 116, Issue: 1, page 1-22
  • ISSN: 0039-3223

Abstract

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A general scheme based on a commutation relation is proposed to give rise to a definition of generalized Toeplitz operators on a Banach space. Under suitable conditions the existence of a symbol is proved and its continuation to algebras generated by generalized Toeplitz operators is constructed. A stability theorem for the point spectrum of an operator from generalized Toeplitz algebras is established; as examples one considers the standard and operator valued Toeplitz operators on weighted Hardy spaces and on spaces of functions (distributions) with weighted l p Fourier transforms.

How to cite

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Nikolskaia, Lioudmila. "Stabilité du spectre ponctuel d'opérateurs de Toeplitz généralisés." Studia Mathematica 116.1 (1995): 1-22. <http://eudml.org/doc/216216>.

@article{Nikolskaia1995,
author = {Nikolskaia, Lioudmila},
journal = {Studia Mathematica},
keywords = {Toeplitz and Wiener-Hopf operators; multipliers; quasi-continuous functions; Wiener-Hopf operators; commutation relation; generalized Toeplitz operators on a Banach space; stability theorem for the point spectrum; Toeplitz operators on weighted Hardy spaces; spaces of functions (distributions) with weighted Fourier transforms},
language = {fre},
number = {1},
pages = {1-22},
title = {Stabilité du spectre ponctuel d'opérateurs de Toeplitz généralisés},
url = {http://eudml.org/doc/216216},
volume = {116},
year = {1995},
}

TY - JOUR
AU - Nikolskaia, Lioudmila
TI - Stabilité du spectre ponctuel d'opérateurs de Toeplitz généralisés
JO - Studia Mathematica
PY - 1995
VL - 116
IS - 1
SP - 1
EP - 22
LA - fre
KW - Toeplitz and Wiener-Hopf operators; multipliers; quasi-continuous functions; Wiener-Hopf operators; commutation relation; generalized Toeplitz operators on a Banach space; stability theorem for the point spectrum; Toeplitz operators on weighted Hardy spaces; spaces of functions (distributions) with weighted Fourier transforms
UR - http://eudml.org/doc/216216
ER -

References

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  1. [1] J. Bergh and J. Löfström, Interpolation Spaces. An Introduction, Springer, 1976. Zbl0344.46071
  2. [2] A. Bottcher and B. Silbermann, Analysis of Toeplitz Operators, Akademie-Verlag, Berlin, 1989. Zbl0689.45009
  3. [3] A. Devinatz and M. Shinbrot, General Wiener-Hopf operators, Trans. Amer. Math. Soc. 145 (1969), 467-494. Zbl0193.10901
  4. [4] R. Douglas, Banach Algebra Techniques in the Theory of Toeplitz Operators, CBMS Regional Conf. Ser. in Math. 15, Amer. Math. Soc., 1973. Zbl0252.47025
  5. [5] R. Douglas, Banach Algebra Techniques in Operator Theory, Academic Press, New York, 1972. Zbl0247.47001
  6. [6] D. A. Herrero, T. J. Taylor and L. V. Wang, Variations of the point spectrum under compact perturbations, dans : Oper. Theory Adv. Appl. 32, Birkhäuser, 1988, 113-157. 
  7. [7] T. Kato, Perturbation Theory for Linear Operators, Springer, 1976. Zbl0342.47009
  8. [8] L. N. Nikol'skaya, Criteria for stability of the point spectrum under completely continuous perturbations, Math. Notes 19 (1975), 946-949. 
  9. [9] L. N. Nikol'skaya, Stability of the eigenvalues of certain types of singular integral equations, J. Soviet Math. 32 (1986), 513-519. 
  10. [10] L. N. Nikol'skaya, Stability of characteristic values of singular integral equations, ibid. 50 (1990), 2027-2031. 
  11. [11] N. Nikolski, Treatise on the Shift Operator, Springer, 1986. 
  12. [12] L. Page, Bounded and compact vectorial Hankel operators, Trans. Amer. Math. Soc. 150 (1970), 529-539. Zbl0203.45701
  13. [13] R. Rochberg, Toeplitz operators on weighted H p spaces, Indiana Univ. Math. J. 26 (1977), 291-298. Zbl0373.47018
  14. [14] M. Rosenblum, Vectorial Toeplitz operators and the Fejér-Riesz Theorem, J. Math. Anal. Appl. 23 (1968), 139-147. Zbl0159.43102
  15. [15] I. Singer, Theory of Bases, Vol. 1, Springer, 1975. 
  16. [16] S. Treil, Geometric aspects of the spectral function theory, dans : Oper. Theory Adv. Appl. 42, Birkhäuser, 1989, 209-280. 
  17. [17] I. E. Verbitski, Sur les multiplicateurs dans les espaces l p pondérés, dans : Propriétés spectrales des opérateurs, Mat. Issled. 45, Shtiintsa, Kishinev, 1977 (en russe). 

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