ON THE SECOND DUAL SPACE OF THE BANACH SPACE OF VECTOR-VALUED LITTLE LIPSCHITZ FUNCTIONS

抄録

Let X be a compact metric space and E be a Banach space. Then lip (X, E) denotes the Banach space of all E-valued little Lipschitz functions on X. We show that lip(X, E)^∗∗ is isometrically isomorphic to the Banach space of E^∗∗-valued Lipschitz functions Lip(X, E^∗∗) under several conditions. Moreover, we describe the isometric isomorphism from lip(X, E)^∗∗ to Lip(X, E^∗∗).