報告人: 劉銳 教授

講座日期：2019-12-06

講座時間：15:30

報告地點：長安校區(qū) 數(shù)學(xué)與信息科學(xué)學(xué)院學(xué)術(shù)交流廳

主辦單位：數(shù)學(xué)與信息科學(xué)學(xué)院

講座人簡介：

劉銳，南開大學(xué)數(shù)學(xué)科學(xué)學(xué)院教授，博士生導(dǎo)師，主持國家自然科學(xué)基金面上項目，近期論文發(fā)表在Memoirs American Mathematical Society、Journal of Functional Analysis、Fundamenta Mathematicae等雜志。

講座簡介：

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 quantum case.