Weak compactness in the space of operator valued measures $M_ba(Σ,(X,Y))$ and its applications

In this note we present necessary and sufficient conditions characterizing conditionally weakly compact sets in the space of (bounded linear) operator valued measures $M_{ba}(Σ,(X,Y))$. This generalizes a recent result of the author characterizing conditionally weakly compact subsets of the space of nuclear operator valued measures $M_{ba}(Σ,₁(X,Y))$. This result has interesting applications in optimization and control theory as illustrated by several examples.