随机赋范模中的Goldstine-Weston定理
The Goldstine-Weston theorem in random normed modules
摘要：
本文将赋范空间上经典的Goldstine-Weston定理推广到随机赋范模上：随机赋范模$(E,\|\cdot\|)$在随机自然嵌入$J$下的象在其双随机共轭空间$E^{**}$中关于$(ε,λ)$弱 * 拓扑是稠密的;若$E$具有可数级联性质，则$J(E)$关于局部$L^{0}$ -凸弱 * 拓扑在$E^{**}$中也是稠密的.
英文摘要：
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 $(ε,λ)$ 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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