关于弱空间理想L类奇异算子的探讨

Some discussions about weak space ideal L-singular operators

首先定义弱空间理想L类奇异算子的概念,举例说明这类算子在一般情况下真包含严格奇异算子类,但在一定条件下二者又是相等的.然后证明了对给定的非平凡空间理想L,这类算子构成一内射闭算子理想WL S,同时给出有界线性算子属于这个算子理想的充要条件.最后得到新的一种由非平凡空间理想生成算子理想的方法.

This paper gives the definition of the weak space ideal ￡-that the class of operators contains strictly singular operators strictly and under some conditions. It shows tiffs nontrivial space ideal ￡. Further the bounded operator being a weak space class of operators forms a closed singular operators, illustrates proves that the two are equal injective operator ideal for a paper gives the necessary and sufficient conditions for a linear ideal ￡-singular operator. In a word, it gives a new method to generate operator ideals by nontrivial space ideals.