The Structure of Triple Derivations on Semisimple Banach ∗-Algebras

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Abstract

Triple derivations on C ∗-algebras and JB ∗-triples had been extensively studied in the literature. In this paper, we characterize the structure of triple derivations on semisimple complex Banach ∗-algebras. In particular, we show that every triple derivation on a semisimple complex Banach ∗-algebra is automatically continuous and is a special kind of generalized derivations. Our theorems improve and generalize some known results for C ∗-algebras obtained in Barton and Friedman (Bounded derivations of JB ∗-triples, Quart. J. Math. Oxford Ser.41 (1990), 255-268), Burgos et al. (Local triple derivations on C ∗-algebras and JB ∗-triples, Bull. Lond. Math. Soc.46 (2014), 709-724) and Burgos et al. (Local triple derivations on C∗-algebras, Comm. Algebra42 (2014), 1276-1286). The analogous result for standard operator ∗-algebras on Hilbert spaces is also described.

Original languageEnglish
Pages (from-to)759-779
Number of pages21
JournalQuarterly Journal of Mathematics
Volume68
Issue number3
DOIs
Publication statusPublished - 2017 Jan 1

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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