STRONG CONVERSE INEQUALITIES

Techniques are developed to obtain strong converse inequalities for various linear approximation processes. This will establish equivalence between the approximating rate of a certain linear process and the appropriate Peetre K-functional. Approximation processes that will be treated have to be saturated as K-functionals are saturated. These general methods will lead to new results on the various trigonometric polynomial approximation processes, on holomorphic semigroups, on Bernstein polynomials and on other commonly used approximation processes.