Abstract
The convergence of the projection method for a block Toeplitz operator with a continuous operator-valued symbol is proved under the natural conditions on the operator involved. The result is based on a general abstract analysis of the convergence of projection methods which is also presented in this paper. For paired block Toeplitz operators a theorem about the convergence of the projection method is proved too.
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References
N.I. Achiezer, Theory of approximation, New York, 1956.
G. Baxter, A norm inequality for a “finite section” Wiener-Hopf equation, Illinois J. Math. 7 (1963), 97–103.
H. Bercovici, Operator theory and arithmetic in H ∞, Math. Survey Monogr. 26, Amer. Math. Soc, Providence, R.I., 1988.
A. Ben-Artzi and I. Gohberg, Fredholm properties of band matrices and dichotomy, in: Topics in operator theory, Constantin Apostol memorial issue, (ed. I. Gohberg), Operator Theory Advances and Applications 32, Birkhäuser Verlag, Basel, 1988, pp. 37–52.
H. Bart, I. Gohberg and M.A. Kaashoek, The coupling method for solving inte?gral equations, in: Topics in operator theory, systems and networks, the Rehovot workshop, (eds. H. Dym and I. Gohberg), Operator Theory Advances and Applications 12, Birkhäuser Verlag, Basel, 1984, pp. 39–73. Addendum, Integral Equations and Operator Theory 8 (1985), 890–891.
A. Böttcher and B. Silbermann, Analysis of Toeplitz operators, Springer Verlag, Berlin, 1990.
A. Böttcher and B. Silbermann, Operator-valued Szegö-Widom limit theorems, this volume.
I. Gohberg, S. Goldberg and M.A. Kaashoek, Classes of Linear Operators, Vol. I, Birkhäuser Verlag, Basel. 1990.
I.C. Gohberg and LA. Fel’dman, Convolution equations and projection methods for their solution, Transl. Math. Monographs 41, Amer. Math. Soc, Providence R.I., 1974.
I. Gohberg and M.A. Kaashoek, Asymptotic formulas of Szegö-Kac-Achiezer type, Asymptotic Analysis 5 (1992), 187–220.
I. Gohberg and M.A. Kaashoek, The band extension on the real line as a limit of discrete band extensions, II. The entropy principle, in: Continuous and discrete Fourier transforms, extension problems and Wiener-Hopf equations (ed. I. Gohberg), Operator Theory Advances and Applications 58, Birkhäuser Verlag, Basel, 1992; pp. 71–92.
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Dedicated to Harold Widom on the occasion of his 60-th birthday, with admiration and friendship
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© 1994 Birkhäuser Verlag
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Gohberg, I., Kaashoek, M.A. (1994). Projection Method for Block Toeplitz Operators With Operator-Valued Symbols. In: Basor, E.L., Gohberg, I. (eds) Toeplitz Operators and Related Topics. Operator Theory Advances and Applications, vol 71. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8543-0_7
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DOI: https://doi.org/10.1007/978-3-0348-8543-0_7
Publisher Name: Birkhäuser, Basel
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