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

Tony Ho; Antonio M. Peralta; Bernard Russo

Ternary Weakly Amenable C-algebras and JB-triples

Operator Algebras 2015-12-11 v1

Authors: Tony Ho , Antonio M. Peralta , Bernard Russo

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.

Keywords

banach algebras c*-algebras weak convergence

Cite

@article{arxiv.1206.0689,
  title  = {Ternary Weakly Amenable C*-algebras and JB*-triples},
  author = {Tony Ho and Antonio M. Peralta and Bernard Russo},
  journal= {arXiv preprint arXiv:1206.0689},
  year   = {2015}
}

Comments

34 pages, to appear in Quarterly Journal of Mathematics