Derivations which are inner as completely bounded maps

Details Derivations which are inner as completely bounded maps Derivations which are inner as completely bounded maps

2009-07-10

arxiv.org/abs/0907.1850v3

Mathematics

Operator Algebras

15 pages

Scientific paper

We consider derivations from the image of the canonical contraction $\theta_A$ from the Haagerup tensor product of a C*-algebra A with itself to the space of completely bounded maps on A. We show that such derivations are necessarily inner if A is prime or if A is quasicentral with Hausdorff primitive spectrum. We also provide an example of a C*-algebra which has outer elementary derivations.

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