C_2(H)上广义导算子

GENERALIED DERIYATIONS ON C_2(H)

本文主要给出了 C_2(H)上广义导算子δ_(A,B)、τ_(A,B)为弱正规算子、Jordon 类算子的充要条件。

Let H be a Hilbert space,B(H) denote the algebra of all boundedlinear operators on H,C_2(H)denote Schmidt—Class,An operator T∈B(H)is Called a weak—normal if [T*T,TT*]=0;An operator T∈B(H) is Calleda Jordan class if T=M+N,M is normal,N^2=0,[M,N]=0,On C_2(H),we denote δ_A,B(X)=AX-XB,λ_A,B(X)=AXB,In this paper,we give somesufficient and Necessary Conditions that δ_A,B、λ_A,B,become weak—normaloperators and Jordan class operators.