Operator-Valued mazur-Orlicz and moment problems in spaces of analytic functions

The aim of the present work is to prove new applications of some earlier general abstract results on the subject to spaces of analytic functions. The Cauchy inequalities are used systematically, as well as constrained extension of linear operators. One gives necessary and sufficient conditions and only sufficient conditions for the existence of solutions of an operator valued moment problem and of Mazur-Orlicz problems. The upper constraint appears naturally from the corresponding computations, while the lower constraint is sometimes the positivity of the solution. Considering Markov moment problem, one solves a concrete interpolation problem with two constraints. In the case of Mazur-Orlicz problems, the interpolation conditions are replaced by the corresponding inequalities mentioned in section 2. Operator valued solutions are obtained.