Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-25T04:46:46.863Z Has data issue: false hasContentIssue false
  • English
  • Français

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, [email protected], [email protected]
B. SILBERMANN
Affiliation:
Department of Mathematics, Chemnitz University of Technology, D09107 Chemnitz, [email protected], [email protected]
Get access

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

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