Approximate Identity and Arens Regularity of Some Banach Algebras
| dc.creator | Azar, Kazem Haghnejad | |
| dc.creator | Riazi, Abdolhamid | |
| dc.date | 2009-04-27 | |
| dc.date.accessioned | 2026-07-07T13:08:55Z | |
| dc.date.available | 2026-07-07T13:08:55Z | |
| dc.description | Let $A$ be a Banach algebra with the second dual $A^{**}$. If $A$ has a bounded approximate identity $(=BAI)$, then $A^{**}$ is unital if and only if $A^{**}$ has a $weak^* bounded approximate $$identity(=W^*BAI)$. If $A$ is Arens regular and $A$ \noindent has a BAI, then $A^*$ factors on both sides. In this paper we introduce new concepts $LW^*W$ and $RW^*W$- property and we show that under certain conditions if $A$ has $LW^*W$ and $RW^*W$- property, then $A$ is Arens regular and also if $A$ is Arens regular, then $A$ has $LW^*W$ and $RW^*W$- property. We also offer some applications of these new concepts for the special algebras $l^1(G), L^1(G), M(G)$, and $A(G)$. | |
| dc.description | 15 page | |
| dc.identifier | https://arxiv.org/abs/0904.4102 | |
| dc.identifier | http://arxiv.org/abs/0904.4102 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/228577 | |
| dc.subject | Functional Analysis | |
| dc.subject | Operator Algebras | |
| dc.subject | 46L06; 46L07; 46L10; 47L25 | |
| dc.title | Approximate Identity and Arens Regularity of Some Banach Algebras | |
| dc.type | text |