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Part of the book series: Operator Theory Advances and Applications ((OT,volume 207))

Abstract

This article discusses Paul Halmos’s crucial work on Toeplitz operators and the consequences of that work.

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References

  1. Alexandra Alemán and Dragan Vukotić, Zero products of Toeplitz operators, Duke Math. J. 148 (2009), 373–403.

    Article  MATH  MathSciNet  Google Scholar 

  2. Sheldon Axler, Factorization of L∞ functions, Ann. Math. 106 (1977), 567–572.

    Article  MathSciNet  Google Scholar 

  3. Sheldon Axler, Sun-Yung A. Chang, and Donald Sarason, Products of Toeplitz operators, Integral Equations Operator Theory 1 1978, 285–309.

    Article  MATH  MathSciNet  Google Scholar 

  4. José Barría and P.R. Halmos, Asymptotic Toeplitz operators, Trans. Am. Math. Soc. 273 (1982), 621–630.

    Article  MATH  Google Scholar 

  5. Arlen Brown and P.R. Halmos, Algebraic properties of Toeplitz operators, J. Reine Angew. Math. 213 (1964), 89–102.

    MathSciNet  Google Scholar 

  6. Carl C. Cowen and John J. Long, Some subnormal Toeplitz operators, J. Reine Angew. Math. 351 (1984), 216–220.

    MATH  MathSciNet  Google Scholar 

  7. Ronald G. Douglas, Banach Algebra Techniques in Operator Theory, Academic Press, 1972; second edition published by Springer, 1998.

    Google Scholar 

  8. Caixing Gu, Products of several Toeplitz operators, J. Funct. Anal. 171 (2000), 483–527.

    Article  MATH  MathSciNet  Google Scholar 

  9. Kun Yu Guo, A problem on products of Toeplitz operators, Proc. Amer. Math. Soc. 124 (1996), 869–871.

    Article  MATH  MathSciNet  Google Scholar 

  10. P.R. Halmos, A glimpse into Hilbert space, Lectures on Modern Mathematics, Vol. I, edited by T.L. Saaty, Wiley, 1963, 1–22.

    Google Scholar 

  11. P.R. Halmos, A Hilbert Space Problem Book, Van Nostrand, 1967; second edition published by Springer, 1982.

    Google Scholar 

  12. P.R. Halmos, I Want to Be a Mathematician, Springer, 1985.

    Google Scholar 

  13. P.R. Halmos, Quadratic interpolation, J. Operator Theory 7 (1982), 303–305.

    MATH  MathSciNet  Google Scholar 

  14. P.R. Halmos, Ten problems in Hilbert space, Bull. Am. Math. Soc. 76 (1970), 887–993.

    Article  MATH  MathSciNet  Google Scholar 

  15. P.R. Halmos, Ten years in Hilbert space, Integral Equations Operator Theory 2 (1979), 529–564.

    Article  MATH  MathSciNet  Google Scholar 

  16. Philip Hartman and Aurel Wintner, The spectra of Toeplitz’s matrices, Amer. J. Math. 76 (1954), 867–882.

    Article  MATH  MathSciNet  Google Scholar 

  17. Elias M. Stein, Interpolation of linear operators, Trans. Am. Math. Soc. 83 (1956), 482–492.

    Article  MATH  Google Scholar 

  18. 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.

    MATH  MathSciNet  Google Scholar 

  19. Harold Widom, On the spectrum of a Toeplitz operator, Pacific J. Math. 14 (1964), 365–375.

    MATH  MathSciNet  Google Scholar 

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Axler, S. (2010). Toeplitz Operators. In: Axler, S., Rosenthal, P., Sarason, D. (eds) A Glimpse at Hilbert Space Operators. Operator Theory Advances and Applications, vol 207. Springer, Basel. https://doi.org/10.1007/978-3-0346-0347-8_9

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