Let $ H $ be a compact subgroup of a locally compact group $ G $ . We first investigate some (operator) (co)homological properties of the Fourier algebra $A(G/H)$ of the homogeneous space $G/H$ such as (operator) approximate biprojectivity and pseudo-contractibility. In particular, we show that $ A(G/H) $ is operator approximately biprojective if and only if $ G/H $ is discrete. We also show that $A(G/H)^{**}$ is boundedly approximately amenable if and only if G is compact and H is open. Finally, we consider the question of existence of weakly compact multipliers on $A(G/H)$ .

中文翻译：

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齐次空间上傅里叶代数的一些同调性质

让 $ H $ 是局部紧群的紧子群 $ G $ . 我们首先研究傅里叶代数的一些（算子）（共）同调性质 $A(G/H)$ 同质空间的 $G/H$ 例如（算子）近似双射性和伪收缩性。特别是，我们表明 $ A(G/H) $ 算子近似双射当且仅当 $ G/H $ 是离散的。我们还表明 $A(G/H)^{**}$ 当且仅当G紧凑且H开了。最后，我们考虑弱紧乘子的存在性问题 $A(G/H)$ .