Band-dominated operators with operator-valued coefficients, their Fredholmproperties and finite sections

The central theme of the present paper are band and band-dominated operator s, i.e. norm limits of band operators. In the first part, we generalize the results from [24] and [25] concerning the Fredholm properties of band-domi nated operators and the applicability of the finite section method go the c ase of operators with operator-valued coefficients. We characterize these p roperties in terms of the limit operators of the given band-dominated opera tor. The main objective of the second part is to apply these results to pse udodifferential operators on cones in R-n which is possible after a suitabl e discretization.