包络对偶巴拿赫代数的$WAP$ -双投射性
$WAP$-biprojectivity of the enveloping dual Banach algebras
摘要：
本文引入了一个新的双投射性概念，称为$WAP$ -$F(\mathcal{A})$的双投射性，它是与巴拿赫代数$\mathcal{A}$相关联的包络对偶巴拿赫代数.我们发现了Connes双投射性、Connes顺应性与这一新概念之间的关系。证明了对给定的对偶巴拿赫代数$\mathcal{A}$，如果$F(\mathcal{A})$是Connes顺从的，则$\mathcal{A}$也是Connes顺从的.对无限交换紧群$G$，证明了卷积巴拿赫代数$F(L^2(G))$不是$WAP$ -双投射的.最后，我们给出了包络对偶巴拿赫代数的一些例子，并研究了它们的$WAP$ -双投射性和Connes相容性.
英文摘要：
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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