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
