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Approximation properties, frames and general dilation theory

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报告人: 刘锐 教授

讲座日期:2019-12-06

讲座时间:15:30

报告地点:长安校区 数学与信息科学学院学术交流厅

主办单位:数学与信息科学学院

讲座人简介:

刘锐,南开澳门美高梅网投电子数学科学学院教授,博士生导师,主持国家自然科学基金面上项目,近期论文发表在Memoirs American Mathematical Society、Journal of Functional Analysis、Fundamenta Mathematicae等杂志。

讲座简介:

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.

 

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