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Amenability and weak amenability of tensor algebras and algebras of nuclear operators

Part of: Topological algebras, normed rings and algebras, Banach algebras

Published online by Cambridge University Press:  09 April 2009

Niels Grønbaek
Niels Grønbaek
Affiliation:
Københavns Universitets Matematiske Institut Universitetsparken 52100 København Ø, Denmark
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Abstract

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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.

MSC classification

Secondary: 46H20: Structure, classification of topological algebras
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 51 , Issue 3 , December 1991 , pp. 483 - 488
Copyright
Copyright © Australian Mathematical Society 1991

References

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