学术报告：Completely bounded approximation property and cb-frames for operator spaces and reduced C*-algebras for discrete groups

中科院数学与系统科学研究院

数学研究所

学术报告会

报告人：刘 锐（南开大学)

题  目：Completely bounded approximation property and cb-frames for operator spaces and reduced C*-algebras for discrete groups

时  间：2016.05.06（星期五）, 11:00--12:00

地  点：数学院南楼N913室

Abstract:

We introduce the concept of cb-frames for operator spaces, and give a concrete cb-frame for the reduced free group C*-algebra C*_r(F_2) which is derived from the in finite convex decomposition of the biorthogonal system. We prove that, in general, a separable operator space has the completely bounded approximation property if and only if it has a cb-frame if and only if it is completely isomorphic to a completely complemented subspace of an operator space with a cb-basis. Therefore, the reduced group C*-algebra has a cb-frame if (and only if) the discrete group is weakly amenable. Finally, we show that, in contrast to Banach space case, there is a separable operator space, which can not be completely isomorphic to a subspace of an operator space with a cb-basis, then introduce a natural question to ask for a local characterization of subspaces of operator spaces with cb-bases. This is recent joint work with Zhong-Jin Ruan (UIUC).