Skip to main content
SpringerLink
Log in

An index theorem for multivariable Toeplitz operators

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

Abstract

Using K-theory, the (highest) index of Fredholm Toeplitz operators on bounded symmetric domains in ℂn is expressed in topological terms.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Atiyah, M. F.: K-Theory, Lecture Notes by D. W. Anderson. New York-Amsterdam: Benjamin 1967.

    Google Scholar 

  2. Berger, C. A., Coburn, L. A., Korányi, A.: Opérateurs de Wiener-Hopf sur les sphères de Lie, C. R. Acad. Sci. Paris 290 (1980), 989–991.

    Google Scholar 

  3. Boutet de Monvel, L.: On the index of Toeplitz operators of several complex variables, Invent. Math. 50 (1979), 249–272.

    Google Scholar 

  4. Coburn, L. A.: Singular integral operators and Toeplitz operators on odd spheres, Indiana Univ. Math. J. 23 (1973), 433–439.

    Google Scholar 

  5. Douglas, R. G.: Banach Algebra Techniques in Operator Theory. New York-San Francisco-London: Academic Press 1972.

    Google Scholar 

  6. Dynin, A.: Inversion problem for singular integral operators: C*-approach, Proc. Natl. Acad. Sci. USA 75 (1978), 4668–4670.

    Google Scholar 

  7. Gohberg, I. C., Krein, M. G.: Systems of integral equations on a half-line with kernels depending on the difference of arguments, Usp. Mat. Nauk. 13 (1958), 3–72 (Russian); Amer. Math. Soc. Transl. 14 (1960), 217–287.

    Google Scholar 

  8. Ise, M.: Realization of irreducible bounded symmetric domain of type (V) Proc. Japan Acad. 45 (1969), 233–237.

    Google Scholar 

  9. Karoubi, M.: K-Theory, An Introduction. Berlin-Heidelberg-New York: Springer 1978.

    Google Scholar 

  10. Korányi, A.: The Poisson integral for generalized half-planes and bounded symmetric domains. Ann. of Math. 82 (1965), 332–350.

    Google Scholar 

  11. Loos, O.: Bounded Symmetric Domains and Jordan Pairs. University of California, Irvine, 1977.

    Google Scholar 

  12. Springer, T. A.: Jordan Algebras and Algebraic Groups. Berlin-Heidelberg-New York: Springer 1973.

    Google Scholar 

  13. Upmeier, H.: Toeplitz operators on bounded symmetric domains, Trans. Amer. Math. Soc. 280 (1983), 221–237.

    Google Scholar 

  14. Upmeier, H.: Toeplitz C*-algebras on bounded symmetric domains, Ann. of Math. 119 (1984), 549–576.

    Google Scholar 

  15. Upmeier, H.: Toeplitz operators and solvable C*-algebras on hermitian symmetric spaces, Bull. Amer. Math. Soc. 11 (1984), 329–332.

    Google Scholar 

  16. Venugopalkrishna, U.: Fredholm operators associated with strongly pseudo-convex domains in ℂn, J. Funct. Anal. 9 (1972), 349–372.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Kansas, 66045, Lawrence, KS, U.S.A.

    Harald Upmeier

Authors
  1. Harald Upmeier
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Research partially supported by NSF-Grant No. DMS-8403631

Rights and permissions

Reprints and permissions

About this article

Cite this article

Upmeier, H. An index theorem for multivariable Toeplitz operators. Integr equ oper theory 9, 355–386 (1986). https://doi.org/10.1007/BF01199351

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01199351

Keywords

Search

Navigation