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Complete positivity of elementary operators

Authors:	Li Jiankui

Institution:	Department of Mathematics, Hunan Normal University, Changsha, Hunan 410081, People's Republic of China

Abstract:	In this paper, we prove that if $\mathcal{S}$ is an -dimensional subspace of , then $\mathcal{S}$ is $(\frac{n}{2}]+1)$ -reflexive, where $\frac{n}{2}]$ denotes the greatest integer not larger than $\frac{n}{2}$ . By the result, we show that if $\Phi ( \cdot )= \sum \limits _{i=1} \limits ^{n} A_{i}( \cdot )B_{i}$ is an elementary operator on a $C^{\ast }$ -algebra $\mathcal{A}$ , then $\Phi$ is completely positive if and only if $\Phi$ is $(\frac{n-1}{2}]+1)$ -positive.

Keywords:	Reflexivity elementary operator complete positivity

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