AX－XB型广义导算子的零空间

The Kernels of Type AX-XB of Generalized Derivations

讨论了广义导算子δ＿（ＡＢ）（δ＿（ＡＢ）（Ｘ）＝ＡＸ－ＸＢ）的零空间，对某些特殊类算子及对有限维Ｈｉｌｂｅｒｔ空间上，给出了使广义导算子δ＿（ＡＢ）的各次零空间相等的一些充要条件．

he kernels of generalized derivations δ_(AB)(X)= AX-XB are studied.Some sufficient and necessary conditions are obtained of the coincidence of the kernels of δ_(AB) of any order for several special kinds of operators,or in the Hilbert spacewith a finite dimension.