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Pourabbas, A. Sahami, S. F. Shariati","submitted_at":"2018-01-10T13:48:27Z","abstract_excerpt":"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.\n  For an infinite commutative compact group $G$, we show that the convolution Banach algebra $F(L^2(G))$ is not $WAP$-biprojective. 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