Convex -closures versus convex norm-closures in dual Banach spaces

Abstract: A subset Y of a dual Banach space is said to have the property if for every -compact subset H of Y. The purpose of this paper is to give a characterization of the property for subsets of a dual Banach space , and to study the behavior of the property with respect to additions, unions, products, whether the closed linear hull has the property when Y does, etc. We show that the property is stable under all these operations in the class of -analytic subsets of . [Copyright &y& Elsevier]