The Hille-Yosida generation theorem for almost surely bounded C₀--semigroups of continuous module homomorphisms¹

2020/03/30 by Xia Zhang, Ming Liu, Zhang, Xia +3
Engineering · Mathematics · #46A19 #46H25 #60B11 #60G20 #Advanced Banach Space Theory #FOS: Mathematics #Functional Analysis (math.FA) #Nonlinear Differential Equations Analysis #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2003.13477

openalex publication_date 2020/03/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we first study some properties peculiar to C₀--semigroups of continuous module homomorphisms and give a characterization for such a C₀--semigroup to be almost surely bounded. Then, based on these, we establish the Hille-Yosida generation theorem for almost surely bounded C₀--semigroups of continuous module homomorphisms, which generalizes some known results. Moreover, the counterexample constructed in this paper also shows that it is necessary to require the almost sure boundedness for such C₀--semigroups.

Citations

• Optimization of conditional convex risk measures

Related

• Generation of relatively uniformly continuous Semigroups on Vector Lattices
• Generation of subordinated holomorphic semigroups via Yosida's theorem
• A Laplace transform approach to C-semigroups on a T_{ε, λ}-complete random normed module
• Semigroup C*-algebras
• Some remarks in C^*- and K-theory