Morita equivalence and stable isomorphism via unitary operators

TL;DR

This paper introduces $\Delta$-equivalence for dual operator systems and demonstrates that weak TRO-equivalence induces stable isomorphisms via unitary operators, with special cases for operator systems.

Contribution

It establishes $\Delta$-equivalence as an equivalence relation and links weak TRO-equivalence to stable isomorphisms through unitary operators, extending to dual operator spaces and systems.

Findings

Weak TRO-equivalence induces stable isomorphism via unitaries.

$\Delta$-equivalence is an equivalence relation for dual operator systems.

Dual operator spaces as bimodules have TRO-equivalent normal CES representations.

Abstract

We define $\Delta$-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 $\Delta$-equivalent dual operator spaces, considered as bimodules over their left and right adjointable multiplier algebras, have TRO-equivalent normal CES representations.