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ON THE APPROXIMATION NUMBERS FOR THE FINITE SECTIONS OF BLOCK TOEPLITZ MATRICES

Published online by Cambridge University Press:  16 March 2006

A. ROGOZHIN  and
B. SILBERMANN
A. ROGOZHIN
Affiliation:
Department of Mathematics, Chemnitz University of Technology, D09107 Chemnitz, GermanyAlexander.Rogozhin@mathematik.tu-chemnitz.de, bernd.silbermann@mathematik.tu-chemnitz.de
B. SILBERMANN
Affiliation:
Department of Mathematics, Chemnitz University of Technology, D09107 Chemnitz, GermanyAlexander.Rogozhin@mathematik.tu-chemnitz.de, bernd.silbermann@mathematik.tu-chemnitz.de
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Abstract

In this paper we discuss the asymptotic distribution of the approximation numbers of the finite sections for a Toeplitz operator $T(a) \in \mathcal{L}(\ell^{p,\mu}_N)$, $1 < p < \infty$ and $\mu \in \mathbb{R}$, with a continuous matrix-valued generating function $a$. We prove that the approximation numbers of the finite sections $T_n(a) = P_n T(a) P_n$ have the $k$-splitting property, provided $T(a)$ is a Fredholm operator on $\ell^{p,\mu}_N$.

Keywords

47B35 (primary)15A1847A5847A7565F20 (secondary)

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Type
Papers
Information
Bulletin of the London Mathematical Society , Volume 38 , Issue 2 , April 2006 , pp. 301 - 313
Copyright
The London Mathematical Society 2006

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Footnotes

This work was supported by the Deutsche Forschungsgemeinschaft, DFG project SI 474110-1.