Bishop性质(β)的局部化(英文)

Localization of Bishop's Property (β)

对算子T的Bishop性质（β）进行“局部化”，得到T的新的集值函数A（T），E1（T），E2（T），C1（T），Cx（T），并讨论它们之间的相互关系以及它们与T的谱结构的关系．借助这些新概念我们得到算子的可分解性与次可分解性的新的充要条件和谱特征．

In this paper, we 'localize'Bishop's property (β) of an operator T to obtain some new set-valued functions A (T), E1 (T),E2(T),C1 (T),C2 (T) of T and discuss their mutual relations and the relations between them and the spectral structure of T. Also,some new necessary and sufficient condition and spectral criterions for decomposability and subdecomposability of operators are given in terms of these new concepts.