关于G-M型Banach空间

On G-M Type Banach Spaces

引入并讨论空间的若干种分解与合成性质 ,在已有的遗传不可分解和商遗传不可分解空间实例的基础上 ,建立起某些类 Gowers-Maurey型 Banach空间的新概念 .证明在一般情况下 ,这些类新型空间上的算子构成特别简单 :在相差一个严格奇异 (或严格余奇异 )算子理想下 ,是数乘算子 .

Some properties of spaces decomposition and compound have been introduced and discussed.Based on some existed examples of hereditarily indecomposable spaces and quotient incompoundable spaces,new conceptes of Gowers-Maureg type Banach spaces are formed.Generally,this kind of new type spaces has the property that every operator an it has the sum of a scalar multiple of the identity and a strictly singular operator (or cosingular operator).