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

 

Complete positivity of elementary operators


Author: Li Jiankui
Journal: Proc. Amer. Math. Soc. 127 (1999), 235-239
MSC (1991): Primary 47B47, 47B49; Secondary 46L05
MathSciNet review: 1458254
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Abstract: In this paper, we prove that if $\mathcal{S}$ is an $n$-dimensional subspace of $L(H)$, 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.


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Additional Information

Li Jiankui
Affiliation: Department of Mathematics, Hunan Normal University, Changsha, Hunan 410081, People’s Republic of China
Address at time of publication: Department of Mathematics, University of New Hampshire, Durham, New Hampshire 03824
Email: jkli@spicerack.sr.unh.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-99-04505-0
PII: S 0002-9939(99)04505-0
Keywords: Reflexivity, elementary operator, complete positivity
Received by editor(s): July 8, 1996
Received by editor(s) in revised form: May 14, 1997
Communicated by: Dale E. Alspach
Article copyright: © Copyright 1999 American Mathematical Society