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*, Translated from the Russian by A. Feinstein. Translations of Mathematical Monographs, Vol. 18, American Mathematical Society, Providence, R.I., 1969. MR**0246142****[2]**J. William Helton and Roger E. Howe,*Integral operators: commutators, traces, index and homology*, Proceedings of a Conference Operator Theory (Dalhousie Univ., Halifax, N.S., 1973) Springer, Berlin, 1973, pp. 141–209. Lecture Notes in Math., Vol. 345. MR**0390829****[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the trace of commutators in the algebra of operators generated by an operator with trace class self-commutator*, 1972 (unpublished).**[4]**Charles E. Rickart,*General theory of Banach algebras*, The University Series in Higher Mathematics, D. van Nostrand Co., Inc., Princeton, N.J.-Toronto-London-New York, 1960. MR**0115101****[5]**Harold Widom,*Asymptotic behavior of block Toeplitz matrices and determinants*, Advances in Math.**13**(1974), 284–322. MR**0409511**, https://doi.org/10.1016/0001-8708(74)90072-3

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

Article copyright:
© Copyright 1975
American Mathematical Society