报告人：刘锐副教授

       南开大学

报告题目：Operator-valued measures, normal maps, and framings on Banach spaces

报告时间：2018年12月15日下午16:00

报告地点：数理楼661

摘要：The connection between operator-valued measures (OVMs) and bounded linear maps indicate that the dilation theory is in general heavily dependent on the Banach space structure of the dilation spaces. This naturally led to new questions concerning special type of dilations. In particular, it is not known whether ultraweakly continuous (normal) maps can be dilated to ultraweakly continuous homomorphisms, which we prove for the case when the domain algebra is an abelian von Neumann algebra, and any OVM with finite p-variation can be dilated to a (but usually non-Hilbertian) projection-valued measure of the same type, by using tensor products and vector measures on Banach spaces. It is different from the ones constructed before by showing that the conventional minimal framing model of a non-trivial redundant framing constructed always contains an isomorphic copy of c_0 subspace, and hence the dilatation does not have the bounded p-variation property.

报告人简介：刘锐，南开大学伟德国际1946源自英国副教授，博士生导师，主持国家自然科学基金面上项目1项，入选南开大学百名青年学科带头人培养计划。南开大学与美国德州农工大学联合培养博士。曾受邀访问了美国德州大学奥斯汀分校、伊利诺伊大学香槟分校、德州农工大学等名校。主要研究方向为泛函分析,空间理论及其应用，在Journal of Functional Analysis, Memoirs American Mathematical Society, Fundamenta Mathematicae等顶级期刊发表论文30余篇。

联系人：程庆进教授

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