报告题目：Linear and nonlinear approximation for operators and Banach spaces with applications

报告简介：In 1971-1973, Enflo constructed the famous example of a separable Banach space which fails the approximation property (AP), and Pełczyński and Johnson etc. obtained that the bounded approximation property (BAP) is equivalent to be a projection of a Schauder basis. In 1999-2000, Casazza, Han and Larson proved that frame decomposition is equivalent to BAP by dilation technique. Since 2014, we systematically developed Banach dilation theory (Memoirs of AMS 2014) for operator-valued (quantum) measures from commutative and non-commutative operator algebras, and solved the duality problem for frames and atomic decompositions of reflexive Banach spaces.

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

报告人：刘锐，南开大学数学科学学院，教授，博士生导师，研究泛函分析空间理论及其应用，本科毕业于陈省身数学试点班（Chern Class），博士公派Texas A&M大学Banach空间领域著名数学家Thomas Schlumprecht联合指导，多篇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）, Fundamenta Mathematicae, J. Fourier Anal. Appl., Studia Math.,中国科学、数学学报等国内外著名期刊，获2022年天津市数学与统计学联合学术年会青年学者奖，入选南开大学百名青年科学带头人与天津市131创新人才计划，先后主持国家自然科学基金项目，曾获天津市数学会青年学术奖，全国泛函分析空间理论联络组与现代分析数学及其应用学术委员会成员，2019年ICCM国际华人数学家大会45分钟报告，曾访问UIUC、UT-Austin、TAMU、UCF等。

报告时间：2023年5月20日（星期六）下午 4:00-5:00

报告地点：扬州大学数学科学学院210会议室

主办单位：扬州大学数学科学学院

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