Approximation of operators in dual spaces by adjoint operators

Abstract

Let X and Y be Banach spaces, and let T : Y * → X * be a linear continuous operator. We discuss the possibility of approximation of T by adjoint operators S * : Y * → X * in the topology of compact convergence in L(Y *, X *) and in the topology of pointwise X × Y *−convergence in L(Y *, X *) and also approximation of the operator T *∣ X : X → Y ** by operators from X to Y in the corresponding topologies. Bibliography: 11 titles.