Metric properties between spheres and balls of Banach spaces

：刘锐（南开大学）
：2023-03-30 15:00
：厦大海韵园数理大楼天元会议室686

报告人：刘锐（南开大学）

时  间：2023年3月30日下午15:00-16:30

地  点：厦大海韵园数理大楼天元会议室686

内容摘要:

Following the Mazur-Ulam property (Cheng 2011), we introduce the Figiel property on isometric embeddings between unit spheres. A quantitative quasi-anti-Lipschitz inequality is obtained for a near-isometric embedding on unit sphere of a Lindenstrauss space. We show that every bijective near-isometry between their unit spheres can be extended to balls, which implies the Mazur-Ulam property. A Banach space is said to have the ball-covering property (Cheng 2006) if its unit sphere can be covered by countably balls off the origin. We give its topological characterization and explore new examples on tensor products and non-commutative spaces of operators.

个人简介：

刘锐，南开大学数学科学学院，教授，博士生导师，研究方向为泛函分析空间理论与相关领域，在Memoirs A.M.S.、Studia Math.、JFA、Fund. Math.、J. Fourier Anal. Appl.等重要期刊发表学术论文30余篇，主持国家自然科学基金面上项目和青年基金，2016年入选南开大学百名青年学科带头人培养计划，2022年获天津市数学与统计联合学会青年学者奖，曾访问TAMU、UT-Austin、UCF、UIUC等国内外多所高校。

 

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