陈诉人: 刘锐 传授
刘锐，南开大学数学迷信学院传授，博士生导师，掌管国度天然迷信基金面上项目，近期论文发布在Memoirs American Mathematical Society、Journal of Functional Analysis、Fundamenta Mathematicae等杂志。
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.