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

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.