Semigroups of continuous module homomorphisms on complex complete random normed modules*

Abstract

In this paper, we are concerned with a bounded strongly continuous semigroup of continuous module homomorphisms on a complex complete random normed module. The main results of this section are a theorem, which establishes a differential equation associated with the bounded s.c. semigroup generalizing a central result in the paper [X. Zhang and M. Liu, On almost surely bounded semigroups of random linear operators, J. Math. Phys., 54:053517, 2013], and a theorem, which is a version of the Hille–Yosida theorem for the contraction semigroup of continuous module homomorphisms on complex complete RN module.