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

MathSciNet review:
2917089

Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 . Moreover, we show that the dual of a unital operator system has the completely positive matrix numerical index if its dimension is greater than . Furthermore, both and have the completely positive matrix numerical index if their dimensions are greater than , where , is a Hilbert space and 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

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.