Mini-workshop on Banach Space Theory

Mini-workshop on Banach Space Theory

2022年11月24日，星期四，上午9:00 -12:00

腾讯会议：926 278 325

报告人：程庆进，厦门大学

报告题目：Quantitative classification of unit spheres

报告摘要：Let E and F be two Banach spaces. We say that their unit spheres are Hölder equivalent if there is a bijection f between their unit spheres such that f and f^-1 are Hölder continuous. In this talk, we will give the following results:

1) Provide some sharp estimates of modulus of the continuity of Mazur map and the generalized Mazur map between two spheres of L_p-spaces, 1<p<∞.

2) Show that for a given 1<p<∞, all (infinite dimensional) sphere sections of the unit sphere of an L_p -space are uniformly Hölder equivalent.

报告人简介：程庆进，厦门大学数学科学学院，教授，博士生导师。研究方向为Banach空间的非线性几何理论及其应用。主持国家及省部级自然科学基金10多项，在J. Convex Anal.、J. Funct. Anal.、Studia Math.等国际期刊上发表SCI学术论文20多篇。

报告人：张文，厦门大学

报告题目：On a Cauchy Problem in Banach Spaces

报告摘要：In this talk, we consider solvability of the Cauchy initial problem dx/dt = f(t, x), x(0) = x₀ in a Banach space X. We generalize Peano’s existence theorem and show that for any infinite dimensional reflexive Banach space X with an unconditional basis, and for all a > 0 there is a bounded nowhere locally Lipschitz function f which is weak-to-weak continuous on some bounded set so that the Cauchy initial problem has a solution x ∈C¹([0, a], X).

报告人简介：张文，厦门大学数学科学学院教授，博士生导师，主要研究Banach空间理论。作为泛函分析导师组成员长期主持几何非线性泛函分析讨论班，指导泛函分析专业硕士、博士研究生学习。持续研究了嵌入问题和球覆盖的相关性质，深入研究了扰动保距映射的稳定性问题和非紧性测度的相关问题。主持国家级及省部级项目5项，并参加一项国家自然科学重点基金。在J. Convex Anal.、J. Funct. Anal.、J. Math. Anal. Appl.、Sci. China Ser. A等国际期刊上发表SCI学术论文20多篇。

报告人：董云柏，湖北大学

报告题目：On the Hyers-Ulam stability of isometries in Banach spaces

报告摘要：In this talk, we first recall the history of the research on the Hyers-Ulam problem. Then we introduce the weak stability formula for nonsurjective isometries and its best estimate constant. We also give some applications of this formula. In particular, we show a result on nonsurjective isometries between some subspaces of real continuous functions.

报告人简介：董云柏，湖北大学数学与统计学学院教授。2011年于厦门大学基础数学专业获理学博士学位。研究方向为泛函分析空间理论。已主持完成国家自然科学基金面上项目及青年项目各一项。在J. Funct. Anal.、J. Operator Theory、Canad. J. Math.等杂志发表学术论文20余篇。