Three sequential properties of dual Banach spaces in the weak* topology

摘要

We present an example of a Banach space X in whose dual the weak* and weak* sequential closures of every bounded convex set coincide but weak* and weak* sequential closures of bounded sets do not necessarily coincide. We also answer a question of Gulisashvili on scalarly measurable functions. (C) 2015 Published by Elsevier B.V.