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arXiv · 1010.4522

The Goldstine-Weston theorem in random normed modules

Guang Shi
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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 $(E,\|\cdot\|)$ under the random natural embedding $J$ is dense in its double random conjugate space $E^{**}$ with respect to the $(\epsilon,\lambda)$ weak star topology; and $J(E)$ is also dense in $E^{**}$ with respect to the locally $L^{0}$-convex weak star topology if $E$ has the countable concatenation property.

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Guang Shi. 2010-10-21. The Goldstine-Weston theorem in random normed modules. https://arxiv.org/abs/1010.4522

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