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arXiv · 1801.03374

$WAP$-biprojectivity of the enveloping dual Banach algebras

S. F. Shariati·A. Pourabbas·A. Sahami
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Abstract

In this paper, we introduce a new notion of biprojectivity, called $WAP$-biprojectivity for $F(\mathcal{A})$, the enveloping dual Banach algebra associated to a Banach algebra $\mathcal{A}$. We find some relations between Connes biprojectivity, Connes amenability and this new notion. We show that, for a given dual Banach algebra $\mathcal{A}$, if $F(\mathcal{A})$ is Connes amenable, then $\mathcal{A}$ is Connes amenable. For an infinite commutative compact group $G$, we show that the convolution Banach algebra $F(L^2(G))$ is not $WAP$-biprojective. Finally, we provide some examples of the enveloping dual Banach algebras and we study their $WAP$-biprojectivity and Connes amenability.

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BibTeXRIS

S. F. Shariati, A. Pourabbas, A. Sahami. 2018-01-10. $WAP$-biprojectivity of the enveloping dual Banach algebras. https://arxiv.org/abs/1801.03374

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