Derivations which are inner as completely bounded maps

2009/07/10 by Ilja Gogić, Gogić, Ilja
Mathematics · #45L57 #46L07 #Advanced Banach Space Theory #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Operator Algebras (math.OA) #math.OA #msc:45L57 #msc:46L07

paper · pdf · doi:10.48550/arxiv.0907.1850

15 pages

openalex publication_date 2009/07/10 · arxiv created 2009/07/14 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/01

Abstract

We consider derivations from the image of the canonical contraction θ_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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