学术报告会：New Versions of Kalton’s theorem for regular operators and homogeneous polynomials on Banach lattices

报告题目：New Versions of Kalton’s theorem for regular operators and homogeneous polynomials on Banach lattices

报  告  人： 卜庆营   （美国密西西比大学   教授）

报告时间：2024年11月14日周四10：00

Zoom会议ID：314 229 1498，密码：555777

Abstract: The well-known Kalton’s theorem characterizes weakly convergent sequences in the space of compact linear operators on Banach spaces. In this talk, we give new versions of Kalton’s theorem for weakly convergent sequences in the space of compact regular linear operators on Banach lattices and in the space of regular homogeneous polynomials on Banach lattices. As applications, we obtain sufficient conditions for the reflexivity of the space of regular linear operators and the space ofregular homogeneous polynomials on Banach lattices. We show that these sufficient conditions are also necessary under the assumption of the bounded regular approximation property. We also show that under some conditions, the reflexivity of , the Banach space of all bounded linear operators from  to , implies the reflexivity of , the Banach lattice of all regular linear operators from  to . However, the converse is not true by constructing an interesting example.

个人简介：

卜庆营，美国密西西比大学数学系教授、博士生导师，1986-1989在哈尔滨工业大学数学系攻读硕士，1989-1992年在哈尔滨工业大学数学系攻读博士 。主要从事Banach 空间理论，Banach Lattice 理论，测度理论，张量积，序列空间和函数空间等的研究。在国际著名数学杂志发表学术论文80余篇，在该领域内取得了世界领先的结果，为Banach 空间几何学的研究作出了贡献。