TY - JOUR
A2 - De Liu, Pei
AU - Tiexin, Guo
PY - 2013
DA - 2013/10/30
TI - On Some Basic Theorems of Continuous Module Homomorphisms between Random Normed Modules
SP - 989102
VL - 2013
AB - 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).
SN - 2314-8896
UR - https://doi.org/10.1155/2013/989102
DO - 10.1155/2013/989102
JF - Journal of Function Spaces and Applications
PB - Hindawi Publishing Corporation
KW -
ER -