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Fakultät für Mathematik
Fakultät für Mathematik
Lindner, Marko : The finite section method and stable subsequences

## Lindner, Marko : The finite section method and stable subsequences

Author(s):
Lindner, Marko
Title:
The finite section method and stable subsequences
Electronic source:
application/pdf
Preprint series:
Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 15, 2008
Mathematics Subject Classification:
 47N40 [ Applications in numerical analysis ] 47L40 [ Limit algebras, subalgebras of $C^*$-algebras ] 65J10 [ Equations with linear operators ]
Abstract:
The purpose of this note is to prove a sufficient and necessary criterion on the stability of a subsequence of the finite section method for a so-called band-dominated operator on $\ell^p(\Z^N,X)$. We hereby generalize previous results into several directions: We generalize the subsequence theorem from dimension $N=1$ (see [Rabinovich/Roch/Silbermann 2006]) to arbitrary dimensions $N\ge 1$. Even for the case of the full sequence, our result is new in dimensions $N>2$ and it corrects a mistake in the literature for $N=2$. Finally, we allow the truncations to be taken by homothetic copies of very general starlike geometries $\Omega\in\R^N$ rather than convex polytopes.
Keywords:
finite sections, stability, limit operator, band-dominated operator
Language:
English
Publication time:
8 / 2008