Matrix ordered operator algebras
Kate JuschenkoStanislav Popovych
46L0546L0747L5547L0747L30$*$-algebrafaithful representationArchimedean orderoperator system
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.
Indiana University Mathematics Journal
2009
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10.1512/iumj.2009.58.3608
10.1512/iumj.2009.58.3608
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Indiana Univ. Math. J. 58 (2009) 1203 - 1218
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