Skip to main content
Log in

Functional models and finite dimensional perturbations of the shift

  • Published:
Integral Equations and Operator Theory Aims and scope Submit manuscript

Abstract

We study finite dimensional perturbations of shift operators and their membership to the classes A m, n appearing in the theory of dual algebras. The results obtained yield informations about the lattice of invariant subspaces via the techniques of Scott Brown.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. C. APOSTOL,Ultraweakly closed operators algebras, J. Operator Theory2 (1979), 49–61.

    Google Scholar 

  2. J.A. BALL and A.LUBIN,On a class of contractive perturbations of restricted shifts, Pacific J. Math63 (1976), 309–324.

    Google Scholar 

  3. C. BENHIDA,Espaces duaux et propriétés (A m, n ), Acta Sci. Math. (Szeged)58 (1993), 431–441.

    Google Scholar 

  4. H. BERCOVICI, C. FOIAS, C. PEARCY,Dual algebras with applications to invariant subspaces and dilation theory, CBMS Regional Conf. Ser. in Math., Vol.56, Amer. Math. Soc., Providence, RI, 1985.

    Google Scholar 

  5. S. BROWN, B. CHEVREAU,Toute contraction à calcul fonctionnel isométrique est réflexive, C.R. Acad. Sci. Paris série I Math.307 (1988), 185–188.

    Google Scholar 

  6. B. CHEVREAU, G. EXNER, C. PEARCY,On the structure of contraction operators III, Michigan Math. J.36 (1989), 29–62.

    Google Scholar 

  7. D.N. CLARK,One dimensional perturbation of restricted shifts, J. Analyse Math.25 (1972), 169–191.

    Google Scholar 

  8. G.R. EXNER, Y.S. JO, I.B. JUNG,C 0 contractions: Dual operator algebras, Jordan models and multiplicity, J.O.T., to appear.

  9. C. FOIAS and A. E. FRAZHO,The Commutant Lifting Approach To Interpolation Problems, Birkhäuser, Basel, 1990.

    Google Scholar 

  10. P.A. FUHRMANN,On a class of finite dimensional contractive perturbations of restricted shifts of finite multiplicity, Israel J. Math16 (1973), 162–176.

    Google Scholar 

  11. Y. NAKAMURA,One-dimensional perturbations of isometries, Integr. Equat. Oper. Th.9 (1986), 286–294.

    Google Scholar 

  12. Y. NAKAMURA,One-dimensional perturbations of the shift, Integr. Equat. Oper. Th.17 (1993), 373–403.

    Google Scholar 

  13. D. SARASON,Nearly invariant subspaces of the backward shift, inContributions to operator theory and its applications, Operator theory: Advances Appl., Vol.35, Birkhäuser, Basel, 1988, 481–493.

    Google Scholar 

  14. YUL. SHMULYAN,Generalized linear fractional transformations of operator balls, Sibirskii Mat. Zh.21, No. 5 (1980), 114–131. [Russian]

    Google Scholar 

  15. C.L. SIEGEL,Symplectic geometry, Amer. J. Math.65 (1943), 1–86.

    Google Scholar 

  16. B. SZ.-NAGY and C. FOIAS,Harmonic Analysis of operators on Hilbert space, North-Holland, Amsterdam, 1970.

    Google Scholar 

  17. D. TIMOTIN,Redheffer products and characteristic functions, J. Math. Anal. Appl.196 (1995), 823–840.

    Google Scholar 

  18. I. VALUŞESCU,The maximal function of a contraction, Acta Sci. Math.42 (1980), 183–188.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Benhida, C., Timotin, D. Functional models and finite dimensional perturbations of the shift. Integr equ oper theory 29, 187–196 (1997). https://doi.org/10.1007/BF01191428

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01191428

1991 Mathematics Subject Classification

Navigation