关于C_2(H)上的初等算子Δ(X)=AXB+MXN

ON THE ELEMENTARY OPERATOR Δ( X) =AXB+MXN ON C_2(H)

设 H为复 Hilbert空间 ,B( H )为 H上所有有界线性算子构成的空间 ,C2 ( H )表示 H上所有Hilbert-Schmidt类算子 ,按 ( X,Y) =tr( Y* X)构成 Hilbert空间 .在 C2 ( H )中 ,定义算子Δ:X→ AXB+MXN.文中给出了算子 Δ为

Let H be a complex Hilbertspace,B(H) the algebra of all bounded linear operators on H,and C2 (H) the Hilbertspace of all Hilbert-Schmidtoperators on H with respectto the Hilbert- Schmidt norm.On C2 (H) ,define an operatorΔ byΔ(X) =AXB+ MXN.In this paper,the au- thors give the sufficient and necessary conditions under which the operatorΔ becomesθ-operator.