  In this paper, we develop approximation error estimates as well as
corresponding inverse inequalities for B-splines of maximum smoothness, where
both the function to be approximated and the approximation error are measured
in standard Sobolev norms and semi-norms. The presented approximation error
estimates do not depend on the polynomial degree of the splines but only on the
grid size.
  We will see that the approximation lives in a subspace of the classical
B-spline space. We show that for this subspace, there is an inverse inequality
which is also independent of the polynomial degree. As the approximation error
estimate and the inverse inequality show complementary behavior, the results
shown in this paper can be used to construct fast iterative methods for solving
problems arising from isogeometric discretizations of partial differential
equations.
