由非超弱紧测度生成的算子半范数  

Semi-norm of Operator Generated by the Measure of Super Weak Noncompactness

作　　者：涂昆 TU Kun(School of Mathematics Sciences,Yangzhou University,Yangzhou,Jiangsu 225002,China)

机构地区：[1]扬州大学数学科学学院数学系,江苏扬州225002

出　　处：《教育教学论坛》2020年第51期349-350,共2页Education And Teaching Forum

基　　金：国家自然科学基金青年基金(NSFC NO.11701501);江苏高校品牌专业建设工程资助项目(数学与应用数学,PPZY2015B109)。

摘　　要：文章由Banach空间中的非超弱紧测度导出对应的连续线性算子空间中的函数σ,证明了σ是算子空间中的半范数。进一步研究了半范数σ和算子范数‖·‖之间的关系,并由此证明了超弱紧算子空间是连续线性算子空间的闭理想。The functionσin the corresponding continuous linear operator space is derived from the measure of super weak noncompactness in the Banach space,which proves that theσis a half norm in the operator space.Further,we study the relationship between the semi-normσand the operator norm‖·‖,and prove that the space of super weak compact operators is a closed ideal of the space of continuous linear operators.

关 键 词：超弱紧测度 超弱紧算子 半范数 算子理想 

分 类 号：O13[理学—数学]