On The Operator Ideals Of Reflexive Singular Classes And Relevant Problems

Master's academic article " On the operator ideals of reflexive singular classes and relevant problems " introduces reflexive singular operator, weak reflexive singular operator,reflexive cosingular operator and weak reflexive cosingular operator, generating the concept of strict singular operator,strict cosingular operator and weak compact operator.It is presented as five sections.The section 1 defines reflexive singular operator and weak reflexive singular operator, obtaining the characters of reflexive singular operator and weak reflexive singular operator.The section 2 proves that weak reflexive singular operator is a closed and general operator ideal. Reflexive singular operator is sealed under salar multiplication and has absorbability.Weak reflexive singular operator is injective operator ideal and the space ideal generated by it is injective space ideal.The section 2 also considers the relations between quasi-maximal subspace and weak reflexive singular operator. The section 3 defines reflexive cosingular operator and weak reflexive cosingular operator, obtaining the characters of reflexive cosingular operator and weak reflexive cosingular operator.We prove if T is a bounded linear operator and its conjugate operator T* is reflexive singular operator,then T is reflexive cosingular operator. The section 4 proves that the weak reflexive cosingular operator is a closed and general operator ideal. Reflexive cosingular operator is sealed under salar multiplication and has absorbability.Weak reflexive cosingular operator is surjective operator ideal and the space ideal generated by it is surjective space ideal.The section 4 also considers the relations between quasi-maximal quotient space and weak reflexive cosingular operator. The section 5 discusses weak compact operator from new angle,obtains some results.