Jordan derivations on semiprime rings. (English) Zbl 0691.16039

Summary: I. N. Herstein has proved that any Jordan derivation on a 2-torsion free prime ring is a derivation. In this paper we prove that Herstein’s result is true in 2-torsion free semiprime rings. This result makes it possible for us to prove that any linear Jordan derivation on a semisimple Banach algebra is continuous, which gives an affirmative answer to the question posed by A. M. Sinclair [in Proc. Am. Math. Soc. 24, 209-214 (1970; Zbl 0175.440)].


16W20 Automorphisms and endomorphisms
16N60 Prime and semiprime associative rings
16W10 Rings with involution; Lie, Jordan and other nonassociative structures
46H05 General theory of topological algebras
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