Integral Equations and Operator Theory

, Volume 41, Issue 1, pp 123–125 | Cite as

One more proof of the Borodin-Okounkov formula for Toeplitz determinants

  • A. Böttcher
short communication


Recently, Borodin and Okounkov [2] established a remarkable identity for Toeplitz determinants. Two other proofs of this identity were subsequently found by Basor and Widom [1], who also extended the formula to the block case. We here give one more proof, also for the block case. This proof is based on a formula for the inverse of a finite block Toeplitz matrix obtained in the late seventies by Silbermann and the author.

MSC 2000



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  1. [1]
    E.L. Basor and H. Widom: On a Toeplitz determinant identity of Borodin and Okounkov.Integral Equations Operator Theory 37 (2000), 397–401.Google Scholar
  2. [2]
    A. Borodin and A. Okounkov: A Fredholm determinant formula for Toeplitz determinants.Integral Equations Operator Theory 37 (2000), 386–396.Google Scholar
  3. [3]
    A. Böttcher and B. Silbermann: Notes on the asymptotic behavior of block Toeplitz matrices and determinants.Math. Nachr. 98 (1980), 183–210.Google Scholar
  4. [4]
    A. Böttcher and B. Silbermann:Analysis of Toeplitz Operators. Springer-Verlag, Berlin, Heidelberg, New York 1990.Google Scholar

Copyright information

© Birkhäuser Verlag 2001

Authors and Affiliations

  • A. Böttcher
    • 1
  1. 1.Fakultät für MathematikTechnische Universität ChemnitzChemnitzGermany

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