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.

Contents Full-Text PDF