Derivations on real and complex JB*-triples

We prove that the real JB*-triple of all bounded linear operators from one real Hilbert space to another of a different dimension has an outer derivation, provided it is infinite dimensional. We prove that an infinite dimensional real spin factor has an outer derivation. We show that the corresponding complexifications also have outer derivations. We prove that every other real or complex Cartan factor has the inner derivation property, that is, all derivations are inner.

(This paper has appeared in J. London Math. Soc. 64 (2001), 85-102.)

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Juan Martínez Moreno <jmmoreno@goliat.ugr.es> Antonio M. Peralta <aperalta@goliat.ugr.es> Bernard Russo <brusso@math.uci.edu>