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arXiv · 1706.07088

Pointwise amenability for dual Banach algebras

Mannane Shakeri·Amin Mahmoodi
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Abstract

We shall develop two notions of pointwise amenability, namely pointwise Connes amenability and pointwise $w^*$-approximate Connes amenability, for dual Banach algebras which take the $w^*$-topology into account. We shall study these concepts for the Banach sequence algebras $\ell^1(\omega)$ and the weighted semigroup algebras $ \ell^{1}(\mathbb{N}_{\wedge},\omega)$. For a weight $\omega$ on a discrete semigroup $S$, we shall investigate pointwise amenability/Connes amenability of $\ell^1(S,\omega)$ in terms of diagonals.

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Mannane Shakeri, Amin Mahmoodi. 2017-06-21. Pointwise amenability for dual Banach algebras. https://arxiv.org/abs/1706.07088

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