由Grothendieck型刻画生成的非超弱紧测度和赋范半群  

Measure of Super Weak Noncompactness Through Grothendieck′s Characterization and Normed Semi-Group

作　　者：涂昆 TU Kun(School of Mathematical Science,Yangzhou University,Yangzhou 225002,China)

机构地区：[1]扬州大学数学科学学院,江苏扬州225002

出　　处：《华侨大学学报（自然科学版）》2021年第3期398-401,共4页Journal of Huaqiao University(Natural Science)

基　　金：国家自然科学基金青年基金资助项目(11701501)。

摘　　要：由超弱紧集的Grothendieck型刻画研究非超弱紧测度的表示,并给出经典的非超弱紧测度的表示方式.定义非超弱紧测度,并研究非超弱紧测度与赋范半群、超自反子空间构成的商空间、算子生成的测度之间的关系.结果表明:非超弱紧测度实质上具有半范数在解析上的特点.Representation of super weak noncompactness measure is studied with the Grothendieck type characterization of super weak compactness sets,and the classical representation of super weak noncompactness measure is given.Giving the definition of super weak noncompactness measure,and the relationship between super weak noncompactness measure and normed semi-group,quotient space constructed by super-reflexive subspace,the measure generated by operators is studied.The results show that the analytic properties of the super weak noncompactness,in fact,are similar to that of semi-norms.

关 键 词：非超弱紧测度 Banach空间 赋范半群 超弱紧集 

分 类 号：O177.2[理学—数学]