The Central Approximation Theorems for the Method of Left Gamma Quasi-Interpolants in L p spaces

The optimal degree of approximation of the method of Gammaoperators G_n in L_p spaces is O(n^-1). In order to obtain much faster convergence, quasi-interpolants G_n^(k) of G_n in the sense of Sablonnière are considered. We show that for fixed k the operator-norms G_n^(k)_p are uniformly bounded in n. In addition to this, for the first time in the theory of quasi-interpolants, all central problems for approximation methods (direct theorem, inverse theorem, equivalence theorem) could be solved completely for the L_p metric. Left Gamma quasi-interpolants turn out to be as powerful as linear combinations of Gammaoperators [6].