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SOME HOMOLOGICAL PROPERTIES OF FOURIER ALGEBRAS ON HOMOGENEOUS SPACES
Published online by Cambridge University Press: 09 November 2020
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 $A(G/H)$ .
MSC classification
- Type
- Research Article
- Information
- Bulletin of the Australian Mathematical Society , Volume 104 , Issue 1 , August 2021 , pp. 132 - 140
- Copyright
- © 2020 Australian Mathematical Publishing Association Inc.
Footnotes
This research for the second author was in part supported by a grant from IPM (no. 99170411).