Ternary weakly amenable C*-algebras and JB*-triples
A Banach algebra is said to be ternary weakly amenable if
every continuous Jordan triple derivation from it 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.
This paper has appeared electronically in Quarterly Journal of
Mathematics, doi: 10.1093/qmath/has032, and in printed form in Quart. J. Math.
64 (2013), no. 4, 1109-1139.
Tony Ho < zh_ho01@yahoo.com >
Antonio M. Peralta < aperalta@ugr.es >
Bernard Russo < brusso@uci.edu >