On Special Properties for Continuous Convex Operators and Related Linear Operators

Abstract

This paper provides a uniform boundedness theorem for a class of convex operators, such as Banach–Steinhaus theorem for families of continuous linear operators. The case of continuous symmetric sublinear operators is outlined. Second, a general theorem characterizing the existence of the solution of the Markov moment problem is reviewed, and a related minimization problem is solved. Convexity is the common point of the two aims of the paper mentioned above.

Keywords

• convex operator
• uniform boundedness
• symmetric operators
• Hahn–Banach type theorems
• Markov moment problems
• constrained minimization