中文摘要：

利用算子A和B在Hilbert空间X和Y上的空间分解,给出具有limλ→0B（λI＋AY）^-1和limλ→0B（A＋λI）^-1形式的极限存在的充分必要条件,并且得到两类极限的相关极限值.同时,对两类极限的相关性质进行进一步的探讨.

英文摘要：

The necessary and sufficient conditions for the existence of the limitations in the forms of limλ→0B（λI＋AY）^-1 and limλ→0B（A＋λI）^-1 are given out by using spatial decomposition of operators Aand Bin Hilbert spaces Xand Y.The correlative limitation values of the two limitations are also obtained.Meantime,a further exploration of relevant properties of the two limitations is carried out.