【讲座题目】 Approximation property and frame decomposition for operators and Banach spaces

【主 讲 人】刘锐 教授

【讲座时间】2022/09/23 星期五下午3:00-4:00

【讲座地点】腾讯会议 ID:105-367-660

【主讲人简介】 刘锐,南开大学数学科学学院教授,博士生导师,研究泛函分析及其应用,本科毕业于南开大学陈省身数学基地班(Chern Class),博士期间公派Texas A&M大学访问Banach空间方向著名数学家Thomas Schlumprecht,至今多篇研究论文发表在泛函分析杂志J. Funct. Anal., Memoirs Amer. Math. Soc.(长篇论文单行本98页,TAMU曾关于该工作举办专题研讨会), Fundamenta Mathematicae, J. Fourier Anal. Appl., Studia Math., 中国科学中英文版、数学学报中英文版等国内外重要数学期刊,入选南开大学百名青年科学带头人计划与天津市131创新人才计划,先后主持国家自然科学基金面上项目2项和青年基金1项,现任全国泛函分析空间理论学术委员会成员与现代分析数学及其应用学术委员会成员。

【讲座内容简介】 In 1971-1973, Enflo constructed the example of a separable Banach space which fails the approximation property (AP), and Pełczyński and Johnson etc. independently obtained that a separable Banach space has the bounded approximation property (BAP) if and only if it can be complemented-embedded into a Banach space with a Schauder basis. In 1999-2000, by dilation technique, Casazza, Han and Larson introduced frames of Banach spaces, and proved that its existence is equivalent to the BAP. Since 2014, we solved the duality problem for Schauder frames and atomic decompositions of reflexive Banach spaces, and systematically developed Banach dilation theory (Memoirs of the AMS). We also obtained the operator space version of the above Pełczyński-Casazza-Han-Larson theorem.

In recent years, the interests on nonlinear theory of Banach spaces keep increasing. The famous Godefroy-Kalton theorem says that the Lipchitz BAP and the BAP are equivalent. By nonlinear Banach dilation technique, we generalize the Godefroy-Kalton equivalence theorem to wider cases on operators and frames of Banach spaces.

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