完备随机赋范模上的连续模同态半群  

On Semigroups of Continuous Module Homomorphisms on Complete Random Normed Modules

作　　者：张霞 刘明[1] Xia ZHANG;Ming LIU(School of Mathematical Sciences,Tiangong University,Tianjin 300387,P.R.China)

机构地区：[1]天津工业大学数学科学学院,天津300387

出　　处：《数学学报（中文版）》2021年第5期773-786,共14页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金资助项目(11301380);教育部人文社科基金资助项目(20YJC790174);天津市自然科学基金资助项目(18JCYBJC18900)。

摘　　要：本文首先利用完备随机赋范模的层次结构研究了一致连续模同态半群与其无穷小生成元之间的关系,并进一步给出几乎处处有界半群的指数刻画.在此基础上,建立几乎处处有界半群的微分和积分公式,推广了经典的结论.同时,用反例说明要求上述半群几乎处处有界的条件是必要的.In this paper,using the stratification structures of complete random normed modules,we first study some relations between the uniformly continuous semigroups of continuous module homomorphisms and their infinitesimal generators,and further give an exponential characterization of such almost surely bounded semigroups.Then,based on this,we establish the differential and integral formulas for such almost surely bounded semigroups,which generalize the classical case.Meantime,the counterexample also shows that it is necessary to require the almost surely bounded assumption for such semigroups.

关 键 词：L^(0)-Lipschitz 随机赋范模 连续模同态半群 指数刻画 

分 类 号：O177.2[理学—数学]