Completely positive matrix numerical index on matrix regular operator spaces

Huang, Xu-Jian

doi:10.1090/S0002-9939-2012-11155-4

Completely positive matrix numerical index on matrix regular operator spaces
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by Xu-Jian Huang PDF

Proc. Amer. Math. Soc. 140 (2012), 3161-3167 Request permission

Abstract:

In the article, we compute the completely positive matrix numerical index of matrix regular operator spaces and show that they take values in the interval $[\frac {1}{2},1]$. Moreover, we show that the dual of a unital operator system has the completely positive matrix numerical index $\frac {1}{2}$ if its dimension is greater than $1$. Furthermore, both $S_p(\mathbf {H})$ and $L_p(\mathbf {M})$ have the completely positive matrix numerical index $2^{-\frac {1}{p}}$ if their dimensions are greater than $1$, where $p\in [1, + \infty )$, $\mathbf {H}$ is a Hilbert space and $\mathbf {M}$ is a finite von Neumann algebra.

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