From linear to nonlinear bounded approximation property for operators and Banach spaces
报告人：刘锐（南开大学）
报告时间：2021年4月29日9:30-10:30
腾讯会议：242-725-896
摘要：
In 1971-1973, Enflo constructed the example of a separable Banach space which fails the approximation property, and Johnson, Rosenthal, Zippin and Pełczyński independently obtained that a separable Banach space has the bounded approximation property (BAP) if and only if it is isomorphic to a complemented subspace of a Banach space with a Schauder basis. In 1999-2000, by the dilation technique for countably atomic case, Casazza, Han and Larson introduced the concept of frames for Banach spaces, and proved that it exists if and only if the space has the BAP. Recently, we solved the reflexivity characterization problem for Schauder frames and atomic decompositions, and systematically developed the general Banach dilation theory from commutative to non-commutative operator-valued measures and strongly continuous operators (Memoirs of the AMS). Moreover, We also proved the operator space version of the above Pełczyński, Casazza, Han and Larson's theorems, and constructed the concrete frame example for reduced free group C*-algebra.
In the past twenty years, the interest on nonlinear approximation properties involving Lipschitz functions and the Lipschitz free spaces keeps increasing. The famous Godefroy-Kalton theorem says that the Lipchitz BAP and the BAP are equivalent for every Banach space, and Godefroy and Ozawa characterized the metric spaces whose free space has the BAP through a Lipschitz analogue of the local reflexivity principle. By the nonlinear dilation technique, we generalize the above Godefroy-Kalton equivalence theorem to wider case on operators and frames for Banach spaces.
专家简介：
刘锐, 南开大学数学科学学院教授, 博士生导师, 从事泛函分析空间理论与相关领域的研究, 已发表多篇研究论文在J. Funct. Anal., Memoirs Amer. Math. Soc., Fundamenta Mathematicae, J. Fourier Anal. Appl., Studia Math., 中国科学, 数学学报, 数学年刊等国内外高水平数学期刊，已获国家自然科学基金面上项目2项和青年基金1项，入选南开大学百名青年学科带头人培养计划和天津市131创新人才计划。
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