Let E and F constitute a Banach pairing. We prove that the algebra of F-nuclear operators on E, Nf (E), is amenable if and only if E is finite dimensional and is weakly amenable if and only if dim KF a‰| 1, and the trace on Ea?—F is injective on KF. Here KF is the kernel of the canonical map Ea?—^F a?’NF(E). On the route we find the corresponding statements for the associated tensor algebra, Ea?—^F.
展开▼
