Some discussions about weak space ideal L-singular operators

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