Fixed point property and the Fourier algebra of a locally compact group
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Bibliographic record
Abstract
We establish some characterizations of the weak fixed point property (weak fpp) for noncommutative (and commutative) $\mathcal {L}^1$ spaces and use this for the Fourier algebra $A(G)$ of a locally compact group $G.$ In particular we show that if $G$ is an IN-group, then $A(G)$ has the weak fpp if and only if $G$ is compact. We also show that if $G$ is any locally compact group, then $A(G)$ has the fixed point property (fpp) if and only if $G$ is finite. Furthermore if a nonzero closed ideal of $A(G)$ has the fpp, then $G$ must be discrete.
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| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.005 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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