【摘 要】
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This talk is on the intersection topics between functional analysis and applied harmonic analysis: 1)We introduce the concept of(Schauder)frames for Banach
【机 构】
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NankaiUniversity,China
【出 处】
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算子代数和调和分析2017年研讨会 (Workshop on Operator Algebras and Harmoni
论文部分内容阅读
This talk is on the intersection topics between functional analysis and applied harmonic analysis: 1)We introduce the concept of(Schauder)frames for Banach and operator spaces,show the connection with the bounded approximation property and complemented embedding,and give the duality theorems for frames and associated basis in reflexive Banach spaces.We give a concrete frame for 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.2)This is on a general dilation theory of operator-valued measures and frames for Banach spaces,motivated by the observation that there is a connection between the analysis of dual pairs of frames(both the discrete and the continuous theory)and the dilation theory of operator-valued measures on Banach spaces.As a continuation of our recent work,we show that every operator-valued system of imprimitivity with a projective isometric group representation has dilation to a spectral system of imprimitivity acting on a larger Banach space,and also prove that every operator-valued measure with bounded p-variation can be dilated to a projection-valued measure with the same variation property on a larger Banach space.
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