Speaker：Rui Liu（Nankai University）

Time：2023-3-30, 15:00

Location：Conference Room 686 at the 6th floor of Shuli Building at Haiyun Campus

Abstract:

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.