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)

Data:	2026
Resum:	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.
Resum:	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
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Llengua:	Anglès
Document:	Article ; recerca ; Versió publicada
Matèria:	Trace space ; Non-unital c∗-algebra ; Pedersen ideal
Publicat a:	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

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