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arXiv · 1206.0689

Ternary Weakly Amenable C*-algebras and JB*-triples

Tony Ho·Antonio M. Peralta·Bernard Russo
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Abstract

A well known result of Haagerup from 1983 states that every C*-algebra A is weakly amenable, that is, every (associative) derivation from A into its dual is inner. A Banach algebra B is said to be ternary weakly amenable if every continuous Jordan triple derivation from B into its dual is inner. We show that commutative C*-algebras are ternary weakly amenable, but that B(H) and K(H) are not, unless H is finite dimensional. More generally, we inaugurate the study of weak amenability for Jordan Banach triples, focussing on commutative JB*-triples and some Cartan factors.

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Tony Ho, Antonio M. Peralta, Bernard Russo. 2012-06-04. Ternary Weakly Amenable C*-algebras and JB*-triples. https://arxiv.org/abs/1206.0689

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