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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(G) is a quantized Banach ordered algebra. It is proved that A(G) is complete order amenable if and only if A(G) is operator amenable. The authors also show that all complete order derivations from A(G) to any dual Banach completely ordered A(G)-bimodule are inner if and only if A(G) is operator amenable.
MSC:
43A07Means on groups, semigroups, etc.; amenable groups
22D15Group algebras of locally compact groups
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