The Goldstine-Weston theorem in random normed modules

2010/10/21 by Guang Shi, Shi, Guang
Mathematics · #FOS: Mathematics #Functional Analysis (math.FA) #math.FA

paper · pdf · doi:10.48550/arxiv.1010.4522

arxiv created 2010/10/21 · arxiv updated 2010/10/22

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,‖⋅‖) under the random natural embedding J is dense in its double random conjugate space E^** with respect to the (ε,λ) weak star topology; and J(E) is also dense in E^** with respect to the locally L⁰-convex weak star topology if E has the countable concatenation property.

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