IUMJ

Title: Matrix ordered operator algebras

Authors: Kate Juschenko and Stanislav Popovych

Issue: Volume 58 (2009), Issue 3, 1203-1218

Abstract:

We study the question when for a given $*$-algebra $\mathcal{A}$ a sequence of cones $C_n\subseteq M_n(\mathcal{A})_{sa}$ can be realized as cones of positive operators in a faithful $*$-representation of $\mathcal{A}$ on a Hilbert space. We present a criterion analogous to Effros-Choi abstract characterization of operator systems. A characterization of operator algebras which are completely boundedly isomorphic to $C\sp*$-algebras is also presented.