弱闭T(N)-模的预零化子的线性等距映象群  

GROUP OF LINEAR ISOMETRIES OF THE PREANNILATORS OF WEAKLY CLOSED T(N)-MODULES

作　　者：骆建文[1] 鲁世杰[2] 

机构地区：[1]上海交通大学管理学院,上海200052 [2]浙江大学数学系,杭州310027

出　　处：《系统科学与数学》2003年第3期426-432,共7页Journal of Systems Science and Mathematical Sciences

基　　金：国家自然科学基金(70271039)

摘　　要：本文刻画了弱闭T(N)-模的预零化子的线性等距映象群的无穷小生成元.设U为由N到N的左连续序同态N到N所确定的弱闭T(N)-模,U_⊥为U的预零化子。{Φ_t :t∈R}为U_⊥到U_⊥上的单参数强连续线性等距映象群。若(0)_*=(0),dim(0)+≠1且H_-=H,dim(HH)≥ 2,则存在有界自伴算子K_1,K_2使得{Φ_t :t∈R}的无穷小生成元为α(X)=i(K_1X-XK_2)。This paper characterizes the infinitesimal generator of a group of linear isometrics on the preannilators of weakly closed T(N)-modules. Let U be the weakly closed T(N)-module determined by the left continuous order homomorphism be a strongly continuous one parameter group of isometrics on U⊥ , where U⊥ is the preannihila-tors of U on a Hilbert space H. We prove that if (0)* = (0), dim(0)≥ 1 and H_ = H, dim(H H) ≠ 2, then the infinitesimal generator of , where K1 and K2 are bounded self-adjiont operators.

关 键 词：“弱闭T(N)-模” 预零化子 线性等距映象群 生成元 强连续酉群 HILBERT空间 算子 

分 类 号：O177[理学—数学]