具有一定谱分解闭算子的判别定理

Sqectaiity Criteria for closed quasi -spectral Operators

本文在[8]的基础上继续探讨闭拟谱算子的特征,得到结果: 定理;iT是(Co)类连续算了群S(t)的无穷小生成元,如果‖S(t)‖≤M(1+.~2)~2(M,n正数);则T是闭拟谱算子,当且仅当,存在常数k,使得,Af∈S,x∈X。

Theorem: it is the infinitesimal generatov of a group of bouuded Operaters S(t). If ||S(t)||≤M(1)t2)2 , Then T is a closed-quasi-spectral Operator, if and only if, k>0 such that