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ArticleOriginal scientific text

Title

Stabilité du spectre ponctuel d'opérateurs de Toeplitz généralisés

Authors 1

Affiliations

  1. UFR de Mathématiques, Université de Bordeaux-1, 351, cours de la Libération, 33405 Talence Cedex, France

Abstract

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 lp Fourier transforms.

Keywords

ENG
Toeplitz and Wiener-Hopf operators, multipliers, quasi-continuous functions

Bibliography

  1. J. Bergh and J. Löfström, Interpolation Spaces. An Introduction, Springer, 1976.
  2. A. Bottcher and B. Silbermann, Analysis of Toeplitz Operators, Akademie-Verlag, Berlin, 1989.
  3. A. Devinatz and M. Shinbrot, General Wiener-Hopf operators, Trans. Amer. Math. Soc. 145 (1969), 467-494.
  4. R. Douglas, Banach Algebra Techniques in the Theory of Toeplitz Operators, CBMS Regional Conf. Ser. in Math. 15, Amer. Math. Soc., 1973.
  5. R. Douglas, Banach Algebra Techniques in Operator Theory, Academic Press, New York, 1972.
  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. T. Kato, Perturbation Theory for Linear Operators, Springer, 1976.
  8. L. N. Nikol'skaya, Criteria for stability of the point spectrum under completely continuous perturbations, Math. Notes 19 (1975), 946-949.
  9. L. N. Nikol'skaya, Stability of the eigenvalues of certain types of singular integral equations, J. Soviet Math. 32 (1986), 513-519.
  10. L. N. Nikol'skaya, Stability of characteristic values of singular integral equations, ibid. 50 (1990), 2027-2031.
  11. N. Nikolski, Treatise on the Shift Operator, Springer, 1986.
  12. L. Page, Bounded and compact vectorial Hankel operators, Trans. Amer. Math. Soc. 150 (1970), 529-539.
  13. R. Rochberg, Toeplitz operators on weighted Hp spaces, Indiana Univ. Math. J. 26 (1977), 291-298.
  14. M. Rosenblum, Vectorial Toeplitz operators and the Fejér-Riesz Theorem, J. Math. Anal. Appl. 23 (1968), 139-147.
  15. I. Singer, Theory of Bases, Vol. 1, Springer, 1975.
  16. S. Treil, Geometric aspects of the spectral function theory, dans : Oper. Theory Adv. Appl. 42, Birkhäuser, 1989, 209-280.
  17. I. E. Verbitski, Sur les multiplicateurs dans les espaces lp pondérés, dans : Propriétés spectrales des opérateurs, Mat. Issled. 45, Shtiintsa, Kishinev, 1977 (en russe).
Studia Mathematica
1995/116/1
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Pages:
1-22
Main language of publication
French
Received
1994-04-21
Accepted
1995-02-09
Published
1995
Exact and natural sciences