, Volume 2, Issue 4, pp 683-699
Date: 15 Jul 2008

Finite Sections of Band-Dominated Operators: l p -Theory

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Abstract.

We propose an algebraic approach to the stability problem for the finite sections of general band-dominated operators acting on \(l^{p} = l^{p}({\mathbb{Z}})\) for 1 < p < ∞. This approach allows us to get new results which previously were known mainly for p = 2. One of the main results shows that a band-dominated operator is Fredholm if and only if the approximation numbers of its finite sections have a special behavior.

In memory of Georgii S. Litvinchuk
Submitted: June 14, 2007. Accepted: November 5, 2007.