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

We propose an algebraic approach to the stability problem for the finite sections of general band-dominated operators acting on 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. Submitted: June 14, 2007. Accepted: November 5, 2007.