On the limit of block Toeplitz determinants

Author:
Harold Widom

Journal:
Proc. Amer. Math. Soc. **50** (1975), 167-173

MSC:
Primary 47B35

DOI:
https://doi.org/10.1090/S0002-9939-1975-0370254-4

MathSciNet review:
0370254

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Abstract: An asymptotic formula is derived for block Toeplitz determinants which generalizes Szegö's well-known formula for ordinary Toeplitz determinants.

**[1]**I. C. Gohberg and M. G. Kreĭn,*Introduction to the theory of linear nonselfadjoint operators*, ``Nauka", Moscow, 1965; English transl., Transl. Math. Monographs, vol. 18, Amer. Math. Soc., Providence, R. I., 1969. MR**36**#3137;**39**#7447. MR**0246142 (39:7447)****[2]**J. W. Helton and R. E. Howe,*Integral operators: traces, index, and homology*, Proc. Conf. on Operator Theory, Lecture Notes in Math., vol. 345, Springer-Verlag, New York, 1973. MR**0390829 (52:11652)****[3]**J. D. Pincus,*On the trace of commutators in the algebra of operators generated by an operator with trace class self-commutator*, 1972 (unpublished).**[4]**C. E. Rickart,*General theory of Banach algebras*, University Series in Higher Math., Van Nostrand, Princeton, N. J., 1960. MR**22**#5903. MR**0115101 (22:5903)****[5]**H. Widom,*Asymptotic behavior of block Toeplitz matrices and determinants*, Advances in Math.**13**(1974), 284-322. MR**0409511 (53:13266a)**

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DOI:
https://doi.org/10.1090/S0002-9939-1975-0370254-4

Article copyright:
© Copyright 1975
American Mathematical Society