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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Completely positive matrix numerical index on matrix regular operator spaces


Author: Xu-Jian Huang
Journal: Proc. Amer. Math. Soc. 140 (2012), 3161-3167
MSC (2010): Primary 46L07, 46L52, 47L07
Published electronically: January 9, 2012
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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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Additional Information

Xu-Jian Huang
Affiliation: Department of Mathematics, Tianjin University of Technology, Tianjin 300384, People’s Republic of China
Email: huangxujian86@gmail.com

DOI: http://dx.doi.org/10.1090/S0002-9939-2012-11155-4
PII: S 0002-9939(2012)11155-4
Keywords: Completely positive matrix numerical index, matrix regular operator space.
Received by editor(s): September 10, 2010
Received by editor(s) in revised form: January 10, 2011, and March 23, 2011
Published electronically: January 9, 2012
Communicated by: Marius Junge
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.