EXTENSION AND DECOMPOSITION OF LINEAR OPERATORS DOMINATED BY CONTINUOUS INCREASING SUBLINEAR OPERATORS

We point out new applications of earlier results on constrained extension of linear operators. In section 2, similar results with respect to previous ones on the Riesz decomposition property, but now for arbitrary linear bounded operators are proved. Increasing continuous sublinear dominating operators play a central role in both sections 2 and 3. In section 3, decomposition as differences of positive bounded linear operators is investigated. Under appropriate assumptions, one proves that the space B(X, Y) of all bounded linear operators from X into Y is an order complete Banach lattice. Finally, section 4 focuses on a constrained optimization problem.