摘要
本文讨论在Banach 空间X 上的闭算子T 和由函数演算所确定的算子f(T)之间的关系.得到下列主要结果:(1) 若f∈(?)_(1/m)(T),且T 是超可分解的,则f(T)也是超可分解的.其中(?)_(1/m)表示在σ(T)的某邻域内解析,且在“∞”处有m 级极点的复值函数.(2) 若f∈(?)_∞(T),且T 是超可分解的,则f(T)也是超可分解的.其中(?)_∞(T)表示在σ(T)∪{∞}的某邻域内解析的复值函数全体.
In this paper,the relations are studied between a ClosedOperators T on Banach Space X and the Operator f(T) defined by thefnnctional Calculus.The main results are as follows:(1) If f∈(?)_(1/m)(T) and T is super-decomposeble,then f(T) also is super-decomposable.(2) If f∈(?)_∞(T) and T is super-decomposable,thenf(T) also is super-decomposable.
出处
《苏州大学学报（自然科学版）》
CAS
1989年第1期18-22,共5页
Journal of Soochow University(Natural Science Edition)
关键词
闭算子
超可分解性
有界线性算子
closed operator
super-decomposable property
bounded linear operator
hyperinvariant subspace
the spectral decomposition property with respect to the identity
