Hermitian crossed product Banach algebras
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866914918905675776 |
|---|---|
| author | Harti, Rachid El Pinto, Paulo R. |
| author_facet | Harti, Rachid El Pinto, Paulo R. |
| contents | We show that the Banach *-algebra $\ell^1(G,A,α)$, arising from a C*-dynamical system $(A,G,α)$, is an hermitian Banach algebra if the discrete group $G$ is finite or abelian (or more generally, a finite extension of a nilpotent group).
As a corollary, we obtain that $\ell^1(\mathbb{Z},C(X),α)$ is hermitian, for every topological dynamical system $Σ= (X, σ)$, where $σ: X\to X$ is a homeomorphism of a compact Hausdorff space $X$ and the action is $α_n(f)=f\circ σ^{-n}$ with $n\in\mathbb{Z}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_11466 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Hermitian crossed product Banach algebras Harti, Rachid El Pinto, Paulo R. Operator Algebras Dynamical Systems Functional Analysis 46L65, 43A20, 54H20, 46K99 We show that the Banach *-algebra $\ell^1(G,A,α)$, arising from a C*-dynamical system $(A,G,α)$, is an hermitian Banach algebra if the discrete group $G$ is finite or abelian (or more generally, a finite extension of a nilpotent group). As a corollary, we obtain that $\ell^1(\mathbb{Z},C(X),α)$ is hermitian, for every topological dynamical system $Σ= (X, σ)$, where $σ: X\to X$ is a homeomorphism of a compact Hausdorff space $X$ and the action is $α_n(f)=f\circ σ^{-n}$ with $n\in\mathbb{Z}$. |
| title | Hermitian crossed product Banach algebras |
| topic | Operator Algebras Dynamical Systems Functional Analysis 46L65, 43A20, 54H20, 46K99 |
| url | https://arxiv.org/abs/2408.11466 |