报告人：刘锐（南开大学）  

时间：2022年05月16日14:00开始

腾讯会议ID：860 512 107

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, partially answered an open question raised by Junge, Ruan and Xu, etc.
      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 Banach dilation technique, we extend the above Godefroy-Kalton equivalence theorem from Banach spaces to wider case on operators.

简介：刘锐，南开大学，数学科学学院，教授，博士生导师。主要从事泛函分析与相关领域研究，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，多篇研究论文在J. Funct. Anal., Memoirs Amer. Math. Soc.， J. Fourier Anal. Appl.发表。

邀请人：黄辉斥

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