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Search: All articles in the CJM digital archive with keyword amenable groups

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1. CJM Online first

Di Nasso, Mauro; Goldbring, Isaac; Jin, Renling; Leth, Steven; Lupini, Martino; Mahlburg, Karl
On a sumset conjecture of Erdős
Erdős conjectured that for any set $A\subseteq \mathbb{N}$ with positive lower asymptotic density, there are infinite sets $B,C\subseteq \mathbb{N}$ such that $B+C\subseteq A$. We verify Erdős' conjecture in the case that $A$ has Banach density exceeding $\frac{1}{2}$. As a consequence, we prove that, for $A\subseteq \mathbb{N}$ with positive Banach density (a much weaker assumption than positive lower density), we can find infinite $B,C\subseteq \mathbb{N}$ such that $B+C$ is contained in the union of $A$ and a translate of $A$. Both of the aforementioned results are generalized to arbitrary countable amenable groups. We also provide a positive solution to Erdős' conjecture for subsets of the natural numbers that are pseudorandom.

Keywords:sumsets of integers, asymptotic density, amenable groups, nonstandard analysis
Categories:11B05, 11B13, 11P70, 28D15, 37A45

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
Category:43A07

3. CJM 2004 (vol 56 pp. 344)

Miao, Tianxuan
Predual of the Multiplier Algebra of $A_p(G)$ and Amenability
For a locally compact group $G$ and $1
Keywords:Locally compact groups, amenable groups, multiplier algebra, Herz algebra
Category:43A07

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