Self-adjoint traces on the Pedersen ideal of C*-algebras
In order to circumvent a fundamental issue when studying densely defined traces on C∗-algebras - which we refer to as the Trace Question - we initiate a systematic study of the set TR(A) of self-adjoint traces on the Pedersen ideal of A. The set TR(A) is a topological vector space with a vector latt...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2026 |
| País: | España |
| Institución: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:324085 |
| Acceso en línea: | https://ddd.uab.cat/record/324085 https://dx.doi.org/urn:doi:10.5565/PUBLMAT7012610 |
| Access Level: | acceso abierto |
| Palabra clave: | Trace space Non-unital c∗-algebra Pedersen ideal |
| Sumario: | In order to circumvent a fundamental issue when studying densely defined traces on C∗-algebras - which we refer to as the Trace Question - we initiate a systematic study of the set TR(A) of self-adjoint traces on the Pedersen ideal of A. The set TR(A) is a topological vector space with a vector lattice structure, which in the unital setting reflects the Choquet simplex structure of the tracial states. We establish a form of Kadison duality for TR(A) and compute TR(A) for principal twisted 'etale groupoid C∗-algebras. We also answer the Trace Question positively for a large class of C∗-algebras. |
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