學術(shù)報告 (2019083)

報告題目：Approximation properties, frames and general dilation theory

報告人：劉銳（南開大學）   

報告時間：2019年11月25日，上午9:30-10:30

報告地點：理學實驗樓312室

報告摘要： We introduce the frames for Banach and operator spaces, show the equivalence with the bounded approximation property and complemented embedding for operator spaces, and give the duality theorems for frames and associated basis in reflexive spaces. We give a concrete example for reduced free group C*-algebra. Motivated by the connection between the analysis of dual pairs of frames (both the discrete and the continuous theory) and general dilation theory of operator-valued measures on Banach spaces, we give the corresponding fundamental dilation theorems for various operator-valued systems, such as, imprimitivity with a projective isometric group action,  OVMs with bounded p-variation. Furthermore, we obtain (Jordan) dilation theorem from commutative vN algebras to non-commutative case.

報告人簡介：劉銳，南開大學數(shù)學科學學院教授，博士生導師，主持國家自然科學基金面上項目，在Memoirs American Mathematical Society,Journal of Functional Analysis， Fundamenta Mathematicae等雜志發(fā)表論文多篇。 

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