Advertisement

Paul Halmos and Toeplitz Operators

  • Sheldon Axler

Abstract

Paul Halmos has written two papers and several snippets about Toeplitz operators. Another of his papers was motivated by a major result in Toeplitz operator theory. This article is the story of Halmos’s work on Toeplitz operators and its influence upon the field.

Keywords

Hilbert Space Toeplitz Operator Main Diagonal Toeplitz Matrix Integral Equation Operator Theory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Sheldon Axler, Factorization of L∞ functions, Ann. Math. 106 (1977), 567–572.MathSciNetMATHCrossRefGoogle Scholar
  2. 2.
    Sheldon Axler, Sun-Yung A. Chang, and Donald Sarason, Products of Toeplitz operators, Integral Equations Operator Theory 1 (1978), 285–309.MathSciNetMATHCrossRefGoogle Scholar
  3. 3.
    José Barria and P.R. Halmos, Asymptotic Toeplitz operators, Trans. Am. Math. Soc. 273 (1982), 621–630.MathSciNetMATHCrossRefGoogle Scholar
  4. 4.
    Arlen Brown and P.R. Halmos, Algebraic properties of Toeplitz operators, J. Reine Angew. Math. 213 (1964), 89–102.MathSciNetGoogle Scholar
  5. 5.
    Carl C. Cowen and John J. Long, Some subnormal Toeplitz operators, J. Reine Angew. Math. 351 (1984), 216–220.MathSciNetMATHGoogle Scholar
  6. 6.
    Ronald G. Douglas, Banach Algebra Techniques in Operator Theory, Academic Press, New York, 1972.MATHGoogle Scholar
  7. 7.
    P.R. Halmos, A glimpse into Hilbert space, Lectures on Modern Mathematics, Vol. I, edited by T.L. Saaty, John Wiley and Sons, New York, 1963, 1–22.Google Scholar
  8. 8.
    P.R. Halmos, A Hilbert Space Problem Book, Van Nostrand Company, Princeton, 1967.MATHGoogle Scholar
  9. 9.
    P.R. Halmos, Ten problems in Hilbert space, Bull. Am. Math. Soc. 76 (1970), 887–993.MathSciNetMATHCrossRefGoogle Scholar
  10. 10.
    P.R. Halmos, Ten years in Hilbert space, Integral Equations Operator Theory 2 (1979), 529–564.MathSciNetMATHCrossRefGoogle Scholar
  11. 11.
    P.R. Halmos, Quadratic interpolation, J. Operator Theory 7 (1982), 303–305.MathSciNetMATHGoogle Scholar
  12. 12.
    P.R. Halmos,I Want to Be a Mathematician, Springer-Verlag, New York, 1985.Google Scholar
  13. 13.
    Elias M. Stein, Interpolation of linear operators, Trans. Am. Math. Soc. 83 (1956), 482–492.MATHCrossRefGoogle Scholar
  14. 14.
    A.L. Volberg, Two remarks concerning the theorem of S. Axler, S.-Y.A. Chang and D. Sarason, J. Operator Theory 7 (1982), 209–218.MathSciNetMATHGoogle Scholar
  15. 15.
    Harold Widom, On the spectrum of a Toeplitz operator, Pacific J. Math. 14 (1964), 365–375.MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1991

Authors and Affiliations

  • Sheldon Axler
    • 1
  1. 1.Department of MathematicsMichigan State UniversityEast LansingUSA

Personalised recommendations