Self-adjoint traces on the Pedersen ideal of C*-algebras
Gabe, James (University of Southern Denmark. Department of Mathematics and Computer Science)
Miller, Alistair (KU Leuven. Department of Mathematics)

Fecha:	2026
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 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.
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 the Choquet simplex structure of thetracial 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.
Nota:	This work was supported by DFF grants 1054-00094B and 1026-00371B
Derechos:	Aquest material està protegit per drets d'autor i/o drets afins. Podeu utilitzar aquest material en funció del que permet la legislació de drets d'autor i drets afins d'aplicació al vostre cas. Per a d'altres usos heu d'obtenir permís del(s) titular(s) de drets.
Lengua:	Anglès
Documento:	Article ; recerca ; Versió publicada
Materia:	Trace space ; Non-unital c∗-algebra ; Pedersen ideal
Publicado en:	Publicacions matemàtiques, Vol. 70, Num. 1 (2026) , p. 277-301 (Articles) , ISSN 2014-4350

Adreça original: https://raco.cat/index.php/PublicacionsMatematiques/article/view/980000003217
DOI: 10.5565/PUBLMAT7012610

25 p, 1.1 MB

El registro aparece en las colecciones:
Artículos > Artículos publicados > Publicacions matemàtiques
Artículos > Artículos de investigación