The finite section method and stable subsequences
The purpose of this paper 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 ℓp (ZN, X). We hereby generalize previous results into several directions: We generalize the subsequence theorem from dimension N = 1 (see Rabinovich, Roch and Silbermann (2008) ) to arbitrary dimensions N ≥ 1; and 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. Moreover, we allow the truncations to be taken by homothetic copies of very general starlike geometries Ω ∈ RN rather than convex polytopes. © 2009 IMACS.
Finite section method