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Amenability and weak amenability of tensor algebras and algebras of nuclear operators
Published online by Cambridge University Press: 09 April 2009
Abstract
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 ≦ 1, and the trace on E⊗F is injective on KF. Here KF is the kernel of the canonical map E⊗^F →NF(E). On the route we find the corresponding statements for the associated tensor algebra, E⊗^F.
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- Research Article
- Information
- Journal of the Australian Mathematical Society , Volume 51 , Issue 3 , December 1991 , pp. 483 - 488
- Copyright
- Copyright © Australian Mathematical Society 1991
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