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(bào)告人：程慶進(jìn)，廈門大學(xué)

報(bào)告題目：Quantitative classification of unit spheres

報(bào)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 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 H?lder equivalent.

報(bào)告人簡介：程慶進(jìn)，廈門大學(xué)數(shù)學(xué)科學(xué)學(xué)院，教授，博士生導(dǎo)師。研究方向?yàn)?/span>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(xué)基金10多項(xiàng)，在J. Convex Anal.、J. Funct. Anal.、Studia Math.等國際期刊上發(fā)表SCI學(xué)術(shù)論文20多篇。

報(bào)告人：張文，廈門大學(xué)

報(bào)告題目：On a Cauchy Problem in Banach Spaces

報(bào)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(bào)告人簡介：張文，廈門大學(xué)數(shù)學(xué)科學(xué)學(xué)院教授，博士生導(dǎo)師，主要研究Banach空間理論。作為泛函分析導(dǎo)師組成員長期主持幾何非線性泛函分析討論班，指導(dǎo)泛函分析專業(yè)碩士、博士研究生學(xué)習(xí)。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(xiàng)目5項(xiàng)，并參加一項(xiàng)國家自然科學(xué)重點(diǎn)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(xué)術(shù)論文20多篇。

報(bào)告人：董云柏，湖北大學(xué)

報(bào)告題目：On the Hyers-Ulam stability of isometries in Banach spaces

報(bào)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(bào)告人簡介：董云柏，湖北大學(xué)數(shù)學(xué)與統(tǒng)計(jì)學(xué)學(xué)院教授。2011年于廈門大學(xué)基礎(chǔ)數(shù)學(xué)專業(yè)獲理學(xué)博士學(xué)位。研究方向?yàn)榉汉治隹臻g理論。已主持完成國家自然科學(xué)基金面上項(xiàng)目及青年項(xiàng)目各一項(xiàng)。在J. Funct. Anal.、J. Operator Theory、Canad. J. Math.等雜志發(fā)表學(xué)術(shù)論文20余篇。