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Peer-reviewedCC BYJournal d Analyse Mathématique

Morita equivalence for operator systems

  • George Eleftherakis1
  • Evgenios T. A. Kakariadis2
  • Ivan G. Todorov3
  1. 1Department of Mathematics, Faculty of Sciences, University of Patras, 26504, Patras, Greece
  2. 2Department of Mathematics, National and Kapodistrian University of Athens, Athens, 1578 84, Greece
  3. 3School of Mathematical Sciences, University of Delaware, 501 Ewing Hall, Newark, DE, 19716, USA
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Abstract

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.

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Cite

BibTeXRIS
BibTeX
@article{eleftherakis2026morita,
  title = {{Morita equivalence for operator systems}},
  author = {George Eleftherakis and Evgenios T. A. Kakariadis and Ivan G. Todorov},
  journal = {Journal d Analyse Mathématique},
  year = {2026},
  month = jul,
  doi = {10.1007/s11854-025-0428-6},
  url = {https://doi.org/10.1007/s11854-025-0428-6},
  note = {CC BY},
}
RIS
TY  - JOUR
TI  - Morita equivalence for operator systems
AU  - George Eleftherakis
AU  - Evgenios T. A. Kakariadis
AU  - Ivan G. Todorov
PY  - 2026
DA  - 2026/07/19
JO  - Journal d Analyse Mathématique
DO  - 10.1007/s11854-025-0428-6
UR  - https://doi.org/10.1007/s11854-025-0428-6
AB  - 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.
SN  - 0021-7670
SN  - 1565-8538
ER  -