The Goldstine-Weston theorem in random normed modules

Abstract

This article generalize the classical Goldstine-Weston theorem on normed spaces to one on random normed modules: the image of a random normed module $(E,\Vert \cdot \Vert )$ under the random natural embedding $J$ is dense in its double random conjugate space $E^{\ast \ast }$ with respect to the $(\epsilon ,\lambda )$ weak star topology; and $J(E)$ is also dense in $E^{\ast \ast }$ with respect to the locally $L^0$-convex weak star topology if $E$ has the countable concatenation property.

References in corpus (1)

• Recent progress in random metric theory and its applications to conditional risk measures