J Austral Math Soc Ser A 51 pp483--488, 1991.

Amenability and Weak Amenability of Tensor Algebras and Algebras of Nuclear Operators

Niels Grønbaek

(Received 8 January 1990; revised 5 April 1990)

Abstract

Let E and F constitute a Banach pairing. We prove that the algebra of F-nuclear operators on E, N_F(E), is amenable if and only if E is finite dimensional and is weakly amenable if and only if dim K_F £ 1, and the trace on EÙÄF is injective on K_F. Here K_F is the kernel of the canonical map EÙÄF ® N_F(E). On the route we find the corresponding statements for the associated tensor algebra, EÙÄF.

1991 AMS Subject Classification: 46H20

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Authors

Niels Grønbaek: Københavns Universitets Matematiske Institut Universitetsparken 5, 2100 København Ø, Denmark.

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Last Modified: Mon Feb 3 9:46:10 2003