完备随机内积模上的Hellinger-Toeplistz定理  

The Hellinger-Toeplistz Theorem in Complete Random Inner Product Modules

作　　者：郭铁信[1] 李克华[1] 

机构地区：[1]厦门大学数学科学学院,福建厦门361005

出　　处：《厦门大学学报（自然科学版）》2006年第1期23-25,共3页Journal of Xiamen University：Natural Science

基　　金：国家自然科学基金(10471115)资助

摘　　要：在新近发展起来的随机共轭空间理论基础上,利用完备随机内积模上的Riesz表示定理,证明了如下结论:设(S,χ)是任一完备随机内积模,T:S→S是S上任一模同态.若XTp,q=Xp,Tq,p,q∈S,那么T是几乎处处有界的.The notion of a complete random inner product module is a random generalization of that of a Hilbert space. The Hellinger-Toeplistz theorem in Hilbert spaces is a basic and useful tool for linear operators. In this paper, the basic theorem was generalized onto complete random inner product modules.and the following conclusion was achieved, i. e.. Let （S, χ） be a complete random inner product module and T： S→ S a module homomorphism such that XTp,q = Xp,Tq, arbitrariness p, q∈S. Then T was almost everywhere bounded. It should be pointed out that the present work is based on the newly-developed theory of random conjugate spaces.in particular on the Riesz representation theorem on complete random inner product modules.

关 键 词：随机内积模 几乎处处有界的线性算子 对称的模同态 

分 类 号：O177.39[理学—数学]