Self-adjoint traces on the Pedersen ideal of C*-algebras

• Autores: James Gabe, Alistair Miller
• Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 70, Nº 1, 2026, págs. 277-301
• Idioma: inglés
• DOI: 10.5565/publmat7012610
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• Resumen

  • 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 t he C hoquet s implex s tructure o f 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