Norms of projectors onto spaces with Riesz bases

摘要

Many important linear operators P:X → y of a linear space X onto a subspace y of X are defined by the minimum problem ‖f - Pf‖ = min{‖f - u: u ∈ y}, f ∈ X, where the norm ‖·‖ on X is induced by an inner product. We study the L_∞-norm of such operators P when y has a Riesz basis β. Then we apply the results in detail to the best L_2- and l_2-approximations for univariate polynomial splines spaces and to Box spline series.