报告人：刘锐
报告题目：Bases, frames, and dilations of operator-valued measures on Banach spaces
时间：6月10日下午3点
地点：X2511
报告摘要：This talk is on the intersection topics between functional analysis and applied harmonic analysis: We introduce the concept of (Schauder) frames for Banach and operator spaces, show the connection with the bounded approximation property and complemented embedding, and give the duality theorems for frames and associated basis in reflexive Banach spaces. A general dilation theory of operator-valued measures and frames for Banach spaces is motivated by the observation that there is a connection between the analysis of dual pairs of frames (both the discrete and the continuous theory) and the dilation theory of operator-valued measures on Banach spaces. As a continuation of our recent work, we show that every operator-valued system of imprimitivity with a projective isometric group representation has dilation to a spectral system of imprimitivity acting on a larger Banach space, and also prove that every operator-valued measure with bounded p-variation can be dilated to a projection-valued measure with the same variation property on a larger Banach space.
报告人简介：刘锐，南开大学数学科学学院副教授，博士生导师 。研究方向：泛函分析，空间理论与应用，论文发表在Memoirs of American Mathematical Society，Journal of Functional Analysis，Fundamenta Mathematicae，Studia Mathematica等国际期刊，曾访问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、中佛罗里达大学，主持国家自然科学基金面上项目，入选南开大学百名青年学科带头人培养计划。
请各位老师和同学积极参加，尤其是泛函分析和调和分析方向的。
