弱闭T(N)-模中C_p空间的等距映射

ISOMETRIES OF C_p SPACE IN WEAKLY CLOSEDT(N)-Modules

刻划了弱闭 T( N) -模中 Schatten类之间的等距线性满映射 .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 .Φ为 U∩Cp 到 W∩Cp( 1≤ p<∞ ,p≠ 2 )上的等距线性映射 .若 ( 0 ) +=( 0 ) ,H- =H且min{ dim( 0 ) * ,dim( 0 ) # ,dim( H H～ ) ,dim( H H∧ ) }≥ 2 ,则存在 H到 H的等距 Ui( i=1 ,2 )及酉算子 Vi( i=1 ,2 ) ,使得 Φ( A) =U1 AV1 * 或 Φ( A) =V2 A* U*2 .

The paper charactrizes the isometries between spaces U∩C p and W∩C p,where U and W are the weakly closed T(N)-modules determined by the left continuous order homomorphism N→ and N→ on a Hilbert space H respectively.It is proved that such isometries are of the form A→U 1AV * 1 or A→V 2A *U * 2,where U i(i=1,2) are isometries acting from onto and V i(i=1,2)are unitary operators,if (0)-+=(0),H--=H and min{dim(0)-*,dim(0)-#,dim(HH-～),dim(HH-∧)}≥2.