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arXiv · 1501.06028

On approximate Connes-amenability of enveloping dual Banach algebras

Ahmad Shirinkalam·A. Pourabbas
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Abstract

For a Banach algebra $ \mathcal{A} $, we introduce various approximate virtual diagonals such as approximate WAP-virtual diagonal and approximate virtual diagonal. For the enveloping dual Banach algebra $ F(\mathcal{A}) $ of $ \mathcal{A} $, we show that $ F(\mathcal{A}) $ is approximately Connes-amenable if and only if $ \mathcal{A} $ has an approximate WAP-virtual diagonal. Further, for a discrete group $ G $, we show that if the group algebra $ \ell^1(G) $ has an approximate WAP-virtual diagonal, then it has an approximate virtual diagonal.

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Ahmad Shirinkalam, A. Pourabbas. 2015-01-24. On approximate Connes-amenability of enveloping dual Banach algebras. https://arxiv.org/abs/1501.06028

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