Mini-workshop on Banach Space Theory
2022年11月24日，星期四，上午9:00 -12:00
騰訊會議：926 278 325
報告人：程慶進，廈門大學
報告題目：Quantitative classification of unit spheres
報告摘要：Let E and F be two Banach spaces. We say that their unit spheres are H?lder equivalent if there is a bijection f between their unit spheres such that f and f-1 are H?lder 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 Lp-spaces, 1<p<∞.
2) Show that for a given 1<p<∞, all (infinite dimensional) sphere sections of the unit sphere of an Lp -space are uniformly H?lder equivalent.
報告人簡介：程慶進，廈門大學數(shù)學科學學院，教授，博士生導師。研究方向為Banach空間的非線性幾何理論及其應(yīng)用。主持國家及省部級自然科學基金10多項，在J. Convex Anal.、J. Funct. Anal.、Studia Math.等國際期刊上發(fā)表SCI學術(shù)論文20多篇。
報告人：張文，廈門大學
報告題目：On a Cauchy Problem in Banach Spaces
報告摘要：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).
報告人簡介：張文，廈門大學數(shù)學科學學院教授，博士生導師，主要研究Banach空間理論。作為泛函分析導師組成員長期主持幾何非線性泛函分析討論班，指導泛函分析專業(yè)碩士、博士研究生學習。持續(xù)研究了嵌入問題和球覆蓋的相關(guān)性質(zhì)，深入研究了擾動保距映射的穩(wěn)定性問題和非緊性測度的相關(guān)問題。主持國家級及省部級項目5項，并參加一項國家自然科學重點基金。在J. Convex Anal.、J. Funct. Anal.、J. Math. Anal. Appl.、Sci. China Ser. A等國際期刊上發(fā)表SCI學術(shù)論文20多篇。
報告人：董云柏，湖北大學
報告題目：On the Hyers-Ulam stability of isometries in Banach spaces
報告摘要：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.
報告人簡介：董云柏，湖北大學數(shù)學與統(tǒng)計學學院教授。2011年于廈門大學基礎(chǔ)數(shù)學專業(yè)獲理學博士學位。研究方向為泛函分析空間理論。已主持完成國家自然科學基金面上項目及青年項目各一項。在J. Funct. Anal.、J. Operator Theory、Canad. J. Math.等雜志發(fā)表學術(shù)論文20余篇。
