【作者】 林丽琼；

【导师】 钟怀杰；

【作者基本信息】 福建师范大学 ， 基础数学， 2005， 硕士

【摘要】 硕士学位论文《关于自反奇异类算子理想及其相关问题》引入了自反奇异算子、弱自反奇异算子、自反余奇异算子和弱自反余奇异算子的概念,推广了严格奇异算子、严格余奇异算子及弱紧算子的概念,分五节对其进行研究. §1定义了自反奇异算子和弱自反奇异算子的概念,得到了自反奇异算子和弱自反奇异算子的特征刻画.§2说明弱自反奇异算子是闭的广义算子理想,而自反奇异算子数乘封闭,且具有吸收性;弱自反奇异算子是内射算子理想,由其生成的空间理想是内射空间理想,以及考虑拟极大子空间与弱自反奇异算子的关系.§3引入了自反余奇异算子和弱自反余奇异算子的概念,得到自反余奇异算子和弱自反余奇异算子的特征刻画;证明了对有界算子T,T~*是自反奇异算子,则T是自反余奇异算子.§4证明了弱自反余奇异算子是广义闭算子理想,自反余奇异算子数乘封闭,具有吸收性;弱自反余奇异算子是满射算子理想,由其生成的空间理想是满射的,以及考虑拟极大商空间与弱自反余奇异算子的关系.§5从新的角度对弱紧算子进行研究,得到一些结果.更多还原

【Abstract】 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.更多还原