Annihilators in the bidual of generalized group algebra of a discrete group
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2022
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866929296674652160 |
|---|---|
| author | Singh, Lav Kumar |
| author_facet | Singh, Lav Kumar |
| contents | In this short note, the second dual of generalized group algebra $(\ell^1(G,\mathcal A),\ast)$ equipped with both Arens products is investigated, where $G$ is any discrete group and $\mathcal A$ is a Banach algebra containing a complemented algebraic copy of $(\ell^1(\mathbb N),\bullet)$. We give an explicit family of annihilators(w.r.t both the Arens product) in the algebra $\ell^1(G,\mathcal A)^{**}$, arising from non-principal ultrafilters on $\mathbb N$ and which are not in the topological center. As a consequence, we also deduce the fact that $\ell^1(G,\mathcal A)$ is not Strongly Arens irregular. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2205_10694 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Annihilators in the bidual of generalized group algebra of a discrete group Singh, Lav Kumar Functional Analysis 43A20, 46B28, 46M05, 46H20 In this short note, the second dual of generalized group algebra $(\ell^1(G,\mathcal A),\ast)$ equipped with both Arens products is investigated, where $G$ is any discrete group and $\mathcal A$ is a Banach algebra containing a complemented algebraic copy of $(\ell^1(\mathbb N),\bullet)$. We give an explicit family of annihilators(w.r.t both the Arens product) in the algebra $\ell^1(G,\mathcal A)^{**}$, arising from non-principal ultrafilters on $\mathbb N$ and which are not in the topological center. As a consequence, we also deduce the fact that $\ell^1(G,\mathcal A)$ is not Strongly Arens irregular. |
| title | Annihilators in the bidual of generalized group algebra of a discrete group |
| topic | Functional Analysis 43A20, 46B28, 46M05, 46H20 |
| url | https://arxiv.org/abs/2205.10694 |