On Some Basic Theorems of Continuous Module Homomorphisms between Random Normed Modules
Author
Source
Journal of Function Spaces and Applications
Issue
Vol. 2013, Issue 2013 (31 Dec. 2013), pp.1-13, 13 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2013-10-30
Country of Publication
Egypt
No. of Pages
13
Main Subjects
Abstract EN
We first prove the resonance theorem, closed graph theorem, inverse operator theorem, and open mapping theorem for module homomorphisms between random normed modules by simultaneously considering the two kinds of topologies—the (ϵ,λ)-topology and the locally L0-convex topology for random normed modules.
Then, for the future development of the theory of module homomorphisms on complete random inner product modules, we give a proof with better readability of the known orthogonal decomposition theorem and Riesz representation theorem in complete random inner product modules under two kinds of topologies.
Finally, to connect module homomorphism between random normed modules with linear operators between ordinary normed spaces, we give a proof with better readability of the known result connecting random conjugate spaces with classical conjugate spaces, namely, Lq(S*)≅(Lp(S))', where p and q are a pair of Hölder conjugate numbers with 1≤p<+∞,S a random normed module, S* the random conjugate space of S,Lp(S)(Lq(S*)) the corresponding Lp (resp., Lq) space derived from S (resp., S*), and (Lp(S))' the ordinary conjugate space of Lp(S).
American Psychological Association (APA)
Tiexin, Guo. 2013. On Some Basic Theorems of Continuous Module Homomorphisms between Random Normed Modules. Journal of Function Spaces and Applications،Vol. 2013, no. 2013, pp.1-13.
https://search.emarefa.net/detail/BIM-513965
Modern Language Association (MLA)
Tiexin, Guo. On Some Basic Theorems of Continuous Module Homomorphisms between Random Normed Modules. Journal of Function Spaces and Applications No. 2013 (2013), pp.1-13.
https://search.emarefa.net/detail/BIM-513965
American Medical Association (AMA)
Tiexin, Guo. On Some Basic Theorems of Continuous Module Homomorphisms between Random Normed Modules. Journal of Function Spaces and Applications. 2013. Vol. 2013, no. 2013, pp.1-13.
https://search.emarefa.net/detail/BIM-513965
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-513965