Morita equivalence and stable isomorphism via unitary operators

Abstract

We define $Δ$-equivalence for dual operator systems and prove that it is an equivalence relation. We show that weak TRO-equivalence of dual operator spaces induces a stable isomorphism between them which is given by multiplication with unitary operators, and in the special case of dual operator systems it is a unitary equivalence. We prove an analogous result for strong TRO-equivalence of operator spaces and for operator systems. Lastly, we show that $Δ$-equivalent dual operator spaces, considered as bimodules over their left and right adjointable multiplier algebras, have TRO-equivalent normal CES representations.