The Embedding Theorem of an L0-Prebarreled Module into Its Random Biconjugate Space. (30th April 2017)

• Record Type: Journal Article
• Authors: Zhang, Xia; Liu, Ming
• Other Names: Hudzik Henryk Academic Editor.
• Is Part Of: Journal of function spaces. Volume 2017(2017)
• Publication Date: 2017-04-30
• Subjects: Function spaces -- Periodicals; 515.7305
• DOI: 10.1155/2017/8520797
• Languages: English
• ISSNs: 2314-8896

Abstract

Abstract : We first prove Mazur's lemma in a random locally convex module endowed with the locally L 0 -convex topology. Then, we establish the embedding theorem of an L 0 -prebarreled random locally convex module, which says that if ( S, P ) is an L 0 -prebarreled random locally convex module such that S has the countable concatenation property, then the canonical embedding mapping J of S onto J ( S ) ⊂ ( S s ⁎ ) s ⁎ is an L 0 -linear homeomorphism, where ( S s ⁎ ) s ⁎ is the strong random biconjugate space of S under the locally L 0 -convex topology.