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

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.