Self-adjoint traces on the Pedersen ideal of $\mathrm{C}^\ast$-algebras
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866915190340059136 |
|---|---|
| author | Gabe, James Miller, Alistair |
| author_facet | Gabe, James Miller, Alistair |
| contents | In order to circumvent a fundamental issue when studying densely defined traces on $\mathrm{C}^\ast$-algebras -- which we refer to as the Trace Question -- we initiate a systematic study of the set $T_{\mathbb R}(A)$ of self-adjoint traces on the Pedersen ideal of $A$.
The set $T_{\mathbb R}(A)$ 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 $T_{\mathbb R}(A)$ and compute $T_{\mathbb R}(A)$ for principal twisted étale groupoid $\mathrm{C}^\ast$-algebras. We also answer the Trace Question positively for a large class of $\mathrm{C}^\ast$-algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_03587 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Self-adjoint traces on the Pedersen ideal of $\mathrm{C}^\ast$-algebras Gabe, James Miller, Alistair Operator Algebras 46L05, 46L35 In order to circumvent a fundamental issue when studying densely defined traces on $\mathrm{C}^\ast$-algebras -- which we refer to as the Trace Question -- we initiate a systematic study of the set $T_{\mathbb R}(A)$ of self-adjoint traces on the Pedersen ideal of $A$. The set $T_{\mathbb R}(A)$ 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 $T_{\mathbb R}(A)$ and compute $T_{\mathbb R}(A)$ for principal twisted étale groupoid $\mathrm{C}^\ast$-algebras. We also answer the Trace Question positively for a large class of $\mathrm{C}^\ast$-algebras. |
| title | Self-adjoint traces on the Pedersen ideal of $\mathrm{C}^\ast$-algebras |
| topic | Operator Algebras 46L05, 46L35 |
| url | https://arxiv.org/abs/2409.03587 |