SOME HOMOLOGICAL PROPERTIES OF FOURIER ALGEBRAS ON HOMOGENEOUS SPACES
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Abstract 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 $A(G/H)$ .
2015 ◽
Vol 26
(08)
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pp. 1550054
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2017 ◽
Vol 28
(10)
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pp. 1750067
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2013 ◽
Vol 65
(5)
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pp. 1005-1019
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2007 ◽
Vol 59
(5)
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pp. 966-980
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2010 ◽
Vol 127
(3)
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pp. 195-206
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1979 ◽
Vol 251
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pp. 39-39
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