2011/03/28 by Shien Zhao, Guang Shi, Zhao, Shien +1
Decision Sciences · Mathematics · #46A16 #46A22 #46H05 #46H25 #FOS: Mathematics #Functional Analysis (math.FA) #Multi-Criteria Decision Making #math.FA #msc:46A16 #msc:46A22 #msc:46H05 #msc:46H25
paper · pdf · doi:10.48550/arxiv.1103.5318
14 pages
openalex publication_date 2011/03/28 · arxiv created 2011/03/29 · arxiv updated 2011/03/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we present a geometric form of the Hahn-Banach extension theorem for L0-linear functions and prove that the geometric form is equivalent to the analytic form of the Hahn-Banach extension theorem. Further, we use the geometric form to give a new proof of a known basic strict separation theorem in random locally convex modules. Finally, using the basic strict separation theorem we establish the Goldstine-Weston theorem in random normed modules under the two kinds of topologies----the (ε,λ)-topology and the locally L0-convex topology, and also provide a counterexample showing that the Goldstine-Weston theorem under the locally L0-convex topology can only hold for random normed modules with the countable concatenation property.