On the geometry of higher duals of a Banach space

Abstract

In this paper we study the geometry of higher duals of a Banach space using techniques from the theory of $M$-ideals. We show that any Banach space that is an $M$-ideal in its bidual is an $M$-ideal in all duals of even order. As a consequence of this result, we show that continuous linear functionals on such spaces have unique norm preserving extensions to all duals of even order.