Journal of Operator Theory

Volume 46, Issue 2, Fall 2001 pp. 381-389.

Reflexivity of finite dimensional subspaces of operators

Authors: Jiankui Li (1), and Zhidong Pan (2)
Author institution: (1) Department of Mathematics, University of New Hampshire, Durham, NH 03824, USA
(2) Department of Mathematics, Saginaw Valley State University, University Center, MI 48710, USA

Summary: We show that any $n$-dimensional subspace of $B(H)$ is $[\sqrt {2n}]$-reflexive, where $[t]$ denotes the largest integer that is less than or equal to $t\in {\bbb R}$. As a corollary, we prove that if $\phi $ is an elementary operator on a $C^\ast$-algebra $\cal A$ with minimal length $l$, then $\phi $ is completely positive if and only if $\phi $ is $\max\{[\sqrt {2(l-1)} ], 1 \}$-positive.

Keywords: Reflexivity of subspace, separating vector, complete positivity

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