Module homomorphisms on random normed modules. (English) Zbl 0858.60012

Guo, Tiexin

Northeast. Math. J. 12, No. 1, 102-114 (1996).

Summary: We first give a completeness theorem of mapping generated random metric spaces. Then we introduce the concept of random normed modules and study module homomorphisms on random normed modules. Finally, based on these discussions, we also give a completeness theorem of the space of all almost surely bounded linear operators, the resonance theorem of module homomorphisms, and the Mackey theorem on random seminormedly determined spaces.

MSC:

60B99	Probability theory on algebraic and topological structures
54E70	Probabilistic metric spaces

Keywords:

mapping generated random metric space; almost surely bounded random linear functional; random normed module; module homomorphism