Abstract. We derive an index formula for band-dominated operators on $l^p({\msbm Z})$ when $1 < p < \infty $ in terms of local indices of their limit operators. This formula is applied to verify the stability of the finite section method for invertible band-dominated operators with slowly oscillating coefficients. Hilbert space versions of these results (partially under further restrictions) were obtained in [9] and [6], respectively.

AMS Subject Classification (1991): 47A53, 65J10

Received March 23, 2004, and in revised form May 3, 2004. (Registered under 5845/2009.)