广州数学大讲坛等七期
第六十五讲——南开大学刘锐教授学术报告
题目：Approximation properties and dilation theory for operators, frames and Banach spaces
时间：2024年10月15日（星期二）下午14:30-15:30
地点：腾讯会议（会议ID:830-733-459 ，会议密码：241015 ）
报告人：刘锐 教授
摘要：During 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 for operator-valued (quantum) measures from commutative and non-commutative operator algebras, and solved the duality problem for frames and atomic decompositions for reflexive Banach spaces and operator spaces.
In recent years, the interests on nonlinear theory 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 with applications on nonlinear frames and samplings.
报告人简介：
刘锐，南开大学数学科学学院教授，博导。主要研究方向为泛函分析及应用，本科毕业于陈省身数学试点班(Chern Class)，博士公派Texas A&M大学泛函分析领域著名数学家Th. Schlumprecht联合指导，在Memoirs A.M.S., Advances in Math., J. Funct. Anal., Sci. China Math., Fund. Math., J. Fourier Anal. Appl., Studia Math.等杂志发表论文多篇。获天津市数学与统计学联合年会青年学者奖，入选南开百青学科带头人，主持多项国家自然科学基金，入选全国泛函分析空间理论学术委员会；教学方面指导研究生论文发表在Advance/JFA/SciChinaMath，指导本科生获评全国大学生创新年会优秀学术论文，发表教改论文在CSSCI检索《数学教育学报》，主持和参加天津市教改重点项目子课题和教育部拔尖计划重点项目。
