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Complete order amenability of the Fourier algebra. (English) Zbl 1217.43001
The authors define complete order amenability and first-order cohomology groups for quantized Banach ordered algebras. Let $G$ be a locally compact group. Then the Fourier algebra $A\left(G\right)$ is a quantized Banach ordered algebra. It is proved that $A\left(G\right)$ is complete order amenable if and only if $A\left(G\right)$ is operator amenable. The authors also show that all complete order derivations from $A\left(G\right)$ to any dual Banach completely ordered $A\left(G\right)$-bimodule are inner if and only if $A\left(G\right)$ is operator amenable.
##### MSC:
 43A07 Means on groups, semigroups, etc.; amenable groups 22D15 Group algebras of locally compact groups
##### References:
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