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<p>We define Δ-equivalence for operator systems and show that it is identical to stable isomorphism. We define Δ-contexts and bihomomorphism contexts and show that two operator systems are Δ-equivalent if and only if they can be placed in a Δ-context, equivalently, in a bihomomorphism context. We show that nuclearity for a variety of tensor products is an invariant for Δ-equivalence and that function systems are Δ-equivalent precisely when they are order isomorphic. We prove that Δ-equivalent operator systems have equivalent categories of representations. As an application, we characterise Δ-equivalence of graph operator systems in combinatorial terms. We examine a notion of Morita embedding for operator systems, showing that mutually Δ-embeddable operator systems have orthogonally complemented Δ-equivalent corners when represented in the double dual of their C*-envelopes.</p>

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Morita equivalence for operator systems

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年7月19日

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  • George K. Eleftherakis,
  • Evgenios T. A. Kakariadis,
  • Ivan G. Todorov

摘要

We define Δ-equivalence for operator systems and show that it is identical to stable isomorphism. We define Δ-contexts and bihomomorphism contexts and show that two operator systems are Δ-equivalent if and only if they can be placed in a Δ-context, equivalently, in a bihomomorphism context. We show that nuclearity for a variety of tensor products is an invariant for Δ-equivalence and that function systems are Δ-equivalent precisely when they are order isomorphic. We prove that Δ-equivalent operator systems have equivalent categories of representations. As an application, we characterise Δ-equivalence of graph operator systems in combinatorial terms. We examine a notion of Morita embedding for operator systems, showing that mutually Δ-embeddable operator systems have orthogonally complemented Δ-equivalent corners when represented in the double dual of their C*-envelopes.