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

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1. 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

2. 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

3. CJM 2002 (vol 54 pp. 795)

Möller, Rögnvaldur G.
Structure Theory of Totally Disconnected Locally Compact Groups via Graphs and Permutations
Willis's structure theory of totally disconnected locally compact groups is investigated in the context of permutation actions. This leads to new interpretations of the basic concepts in the theory and also to new proofs of the fundamental theorems and to several new results. The treatment of Willis's theory is self-contained and full proofs are given of all the fundamental results.

Keywords:totally disconnected locally compact groups, scale function, permutation groups, groups acting on graphs
Categories:22D05, 20B07, 20B27, 05C25

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