Korean J. Math. Vol. 26 No. 2 (2018) pp.285-291
DOI: https://doi.org/10.11568/kjm.2018.26.2.285

A characterization of additive derivations on C∗-algebras

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Published: Jun 30, 2018
Keywords:
additive derivations, biadditive map, jordan derivations.
Mathematics Subject Classification:
46J10, 47B48.

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Ali Taghavi
Department of Mathematics Faculty of Mathematical Sciences University of Mazandaran P. O. Box 47416-1468, Babolsar, Iran.
Aboozar Akbari
Department of Mathematics Faculty of Mathematical Sciences University of Mazandaran P. O. Box 47416-1468, Babolsar, Iran.

Abstract

Let A be a unital C∗-algebra. It is shown that additive map δ:A→A which satisfies
δ(|x|x)=δ(|x|)x+|x|δ(x),  ∀x∈AN
is a Jordan derivation on A. Here, AN is the set of all normal elements in A. Furthermore, if A is a semiprime C∗-algebra then
δ is a derivation.



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