弱闭T(N)-模的预零化子的等距映射

Isometries of the Preannihilators of Weakly Closed T(N)-Modules

本文刻划了弱闭T(N)-模的预零化子间的等距映射.设u,w分别为由左连续序同态N→N和N→N所确定的弱闭T(N)-模,u⊥,w⊥分别为u,w的预零化子,Φ为由u⊥到w⊥上的线性等距映射.若(0)*＝(0)#＝(0),dim(0)+≠1且min{dim(H H),dim(H H)}≥2,则存在酉算子Ui,Vi(i＝1,2),使得Φ(A)＝U1AV*1或Φ(A)＝U2A*V2*.

In this paper, we characterize the linear surjective isometrics between the preannihilators of weakly closed T(N)-modules. Let U and W be the weakly closed T(N)-modules determined by the left order homomorphisms N → N and N→N respectively, and let U(?) and W(?) be the preannihilators of U and W on a Hilbert space H respectively. We prove that the onto isometrics between the spaces U(?) and W(?) are of the form A→U1AV1* or A → U2A*V2, where Ui and Vi (i = 1,2) are unitary operators, if (0)* = (0)# = (0), dim(0)+ ≠ 1 and min{dim(H(?)H), dim(H(?) H)} ≥ 2.