Frame Approximation and Complemented Embedding for Banach and Operator Spaces

Rui Liu

*(Nankai University)*

10:20 am-11:20 am, November 24, 2016 Science Building A1510

__Abstract:__

We introduce the concept of (completely bounded) frames for Banach and operator spaces, show the connection with the (completely) bounded approximation property and complemented embedding, and give the duality theorems for frames and associated bases in Banach spaces. We construct a concrete example of a completely bounded frame in reduced free group C*-algebra, and also prove that a separable operator space has the completely bounded approximation property if and only if it has a completely bounded frame if and only if it is completely isomorphic to a completely complemented subspace of an operator space with a completely bounded basis.

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