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Search: All articles in the CJM digital archive with keyword Arens product

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1. CJM Online first

Ghahramani, F.; Zadeh, S.
Bipositive isomorphisms between Beurling algebras and between their second dual algebras
Let $G$ be a locally compact group and let $\omega$ be a continuous weight on $G$. We show that for each of the Banach algebras $L^1(G,\omega)$, $M(G,\omega)$, $LUC(G,\omega^{-1})^*$ and $L^1(G,\omega)^{**}$, the order structure combined with the algebra structure determines the weighted group.

Keywords:locally compact group, Beurling algebra, Arens product, topological group isomorphism, bipositive algebra isomorphism
Categories:43A20, 43A22

2. CJM 2009 (vol 61 pp. 382)

Miao, Tianxuan
Unit Elements in the Double Dual of a Subalgebra of the Fourier Algebra $A(G)$
Let $\mathcal{A}$ be a Banach algebra with a bounded right approximate identity and let $\mathcal B$ be a closed ideal of $\mathcal A$. We study the relationship between the right identities of the double duals ${\mathcal B}^{**}$ and ${\mathcal A}^{**}$ under the Arens product. We show that every right identity of ${\mathcal B}^{**}$ can be extended to a right identity of ${\mathcal A}^{**}$ in some sense. As a consequence, we answer a question of Lau and \"Ulger, showing that for the Fourier algebra $A(G)$ of a locally compact group $G$, an element $\phi \in A(G)^{**}$ is in $A(G)$ if and only if $A(G) \phi \subseteq A(G)$ and $E \phi = \phi $ for all right identities $E $ of $A(G)^{**}$. We also prove some results about the topological centers of ${\mathcal B}^{**}$ and ${\mathcal A}^{**}$.

Keywords:Locally compact groups, amenable groups, Fourier algebra, identity, Arens product, topological center

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