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arXiv · 1702.04409

Central Beurling algebras: Weak amenability of the central Beurling algebras on [FC]$^-$ groups

Varvara Shepelska·Yong Zhang
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Abstract

We study weak amenability of central Beurling algebras $ZL^1(G,\omega)$. The investigation is a natural extension of the known work on the commutative Beurling algebra $L^1(G,\omega)$. For [FC]$^-$ groups we establish a necessary condition and for [FD]$^-$ groups we give sufficient conditions for the weak amenability of $Z\L1o$. For a compactly generated [FC]$^-$ group with the polynomial weight $\omega_\alpha(x) = (1 + |x|)^\alpha$, we prove that $ZL^1(G,\omega_\alpha)$ is weakly amenable if and only if $\alpha < 1/2$.

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Varvara Shepelska, Yong Zhang. 2017-02-14. Central Beurling algebras: Weak amenability of the central Beurling algebras on [FC]$^-$ groups. https://arxiv.org/abs/1702.04409

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