报告题目：Three kinds of dentabilities in Banach spaces

报告人：张子厚（上海工程技术大学）

时间：2024年11月11日（周一）下午4:00-5:30

地点：数理楼145报告厅

报告摘要：In this talk, firstly we study some kinds of dentabilities in Banach spaces which are closely related to the famous Radon-Nikodym property. We introduce the concepts of the weak*-weak* denting point of a set, which are the generalizations of weak* denting point of a set in dual Banach spaces. By use of the weak*-weak denting point, we characterize the very smooth space, the point of weak*-weak continuity and the extreme point of a unit ball in dual Banach space, respectively.Meanwhile, wealso characterize approximatively weak compact Chebyshev set in dual Banach spaces. Moreover, we defined the nearly weak dentability in Banach spaces, which is a generalization ofthenear dentability. We proved that the necessary and sufficient conditions of the reflexivity by nearly weak dentability. We also obtain that nearly weak dentability is equivalent to both approximatively weak compactness of Banach spaces and w-strong proximinality of every closed convex subset of Banach spaces.

报告人简介：张子厚，上海工程技术大学教授，博士，美国《数学评论》评论员。长期从事Banach空间几何理论与应用及逼近论方面的研究，主持和主要参与六项国家自然科学基金项目。在包括《J. Approx. Theory》、《Nonlinear Analysis. TMA》、《J.Math Anal Appl》《Studia Math》、《Houston J. Math》、《RACSAM》、《Acta Math Sin》、《Acta Math Sci》、《中国科学·数学》等重要刊物在内的杂志上发表论文70余篇。在科学出版社出版列入大学数学科学丛书的学术专著一部、在高教出版社出版教材两部。排名第一分别获得上海市自然科学奖一项、上海市教学成果奖两项。主持完成上海市教委重点课程一门。曾任2018年国家自然科学奖会评专家，荣获上海市育才奖，宝钢优秀教师奖等多项称号。