赋范空间上紧线性算子零空间的性质

Naught space properties of compact linear operator in normed space

在赋范空间中,紧线性算子T的零空间有2个性质:(1)对每一非零的特征值,Tλ=T-λI的零空间是N(Tλ)为有限维的;(2)总存在一正整数r使得对大于r的所有整数n,N(Tnλ)都相等,证明了这2个性质的假设条件还可减弱。

In normed space,the naught space of compact linear operator T has two properties:first,the naught space N(Tλ) of operator Tλ=T-λI is a finite dimension for every nonzero eigenvalue;second,there is a positive integeral number r such that N(Tnλ) is equal for every integeral number n which is larger than r.It is proved that postulates on the two properties can be weaken.