Weakly Parametric Pseudodifferential Calculus for Twisted $C^*$-dynamical Systems
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2023
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866911873406861312 |
|---|---|
| author | Lee, Gihyun Lesch, Matthias |
| author_facet | Lee, Gihyun Lesch, Matthias |
| contents | For a twisted $C^*$-dynamical system $(\mathscr{A},\mathbb{R}^n,α,e)$ over a unital $C^*$-algebra we establish a weakly parametric pseudodifferential calculus analogously to the celebrated weakly parametric calculus due to Grubb and Seeley. If the $C^*$-algebra $\mathscr{A}$ has an $α$-invariant trace then we prove an expansion of the resolvent trace (with respect to the dual trace on multipliers) for suitable pseudodifferential multipliers. The question whether the expansion holds true as a Hilbert space trace expansion in concrete GNS spaces for $\mathscr{A}$ will be addressed in a future publication. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_00435 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Weakly Parametric Pseudodifferential Calculus for Twisted $C^*$-dynamical Systems Lee, Gihyun Lesch, Matthias Operator Algebras Functional Analysis Quantum Algebra Primary 46L87, 47G30, Secondary 58B34, 35S99 For a twisted $C^*$-dynamical system $(\mathscr{A},\mathbb{R}^n,α,e)$ over a unital $C^*$-algebra we establish a weakly parametric pseudodifferential calculus analogously to the celebrated weakly parametric calculus due to Grubb and Seeley. If the $C^*$-algebra $\mathscr{A}$ has an $α$-invariant trace then we prove an expansion of the resolvent trace (with respect to the dual trace on multipliers) for suitable pseudodifferential multipliers. The question whether the expansion holds true as a Hilbert space trace expansion in concrete GNS spaces for $\mathscr{A}$ will be addressed in a future publication. |
| title | Weakly Parametric Pseudodifferential Calculus for Twisted $C^*$-dynamical Systems |
| topic | Operator Algebras Functional Analysis Quantum Algebra Primary 46L87, 47G30, Secondary 58B34, 35S99 |
| url | https://arxiv.org/abs/2307.00435 |