Symmetrized pseudofunction algebras from $L^p$-representations and amenability of locally compact groups
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866910695642103808 |
|---|---|
| author | Elkiær, Emilie Mai |
| author_facet | Elkiær, Emilie Mai |
| contents | We show via an application of techniques from complex interpolation theory how the $L^p$-pseudofunction algebras of a locally compact group $G$ can be understood as sitting between $L^1(G)$ and $C^*(G)$. Motivated by this, we collect and review various characterizations of group amenability connected to the $p$-pseudofunction algebra of Herz and generalize these to the symmetrized setting. Along the way, we describe the Banach space dual of the symmetrized pseudofuntion algebras on $G$ associated with representations on reflexive Banach spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_07710 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Symmetrized pseudofunction algebras from $L^p$-representations and amenability of locally compact groups Elkiær, Emilie Mai Functional Analysis Group Theory Operator Algebras We show via an application of techniques from complex interpolation theory how the $L^p$-pseudofunction algebras of a locally compact group $G$ can be understood as sitting between $L^1(G)$ and $C^*(G)$. Motivated by this, we collect and review various characterizations of group amenability connected to the $p$-pseudofunction algebra of Herz and generalize these to the symmetrized setting. Along the way, we describe the Banach space dual of the symmetrized pseudofuntion algebras on $G$ associated with representations on reflexive Banach spaces. |
| title | Symmetrized pseudofunction algebras from $L^p$-representations and amenability of locally compact groups |
| topic | Functional Analysis Group Theory Operator Algebras |
| url | https://arxiv.org/abs/2411.07710 |