Morita equivalence for operator systems
Abstract
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.
Fields of Study & Subjects
Advanced Operator Algebra Research
Advanced Topics in Algebra
Algebraic structures and combinatorial models
Publication details
- Journal / source
- Journal d Analyse Mathématique
- Publisher
- Springer Science and Business Media LLC
- Volume
- 159
- Issue
- 2
- Pages
- 401–463
- Publication date
- 19 July 2026
- Language
- EN