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(He(?)^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.