Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
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JORDAN DERIVATIONS ON SEMIPRIME RINGS AND THEIR RADICAL RANGE IN BANACH ALGEBRAS

  • Kim, Byung Do (Department of Mathematics Gangneung-Wonju National University)
  • Received : 2017.06.15
  • Accepted : 2017.09.30
  • Published : 2018.02.15
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Abstract

Let R be a 3!-torsion free noncommutative semiprime ring, and suppose there exists a Jordan derivation $D:R{\rightarrow}R$ such that $D^2(x)[D(x),x]=0$ or $[D(x),x]D^2(x)=0$ for all $x{\in}R$. In this case we have $f(x)^5=0$ for all $x{\in}R$. Let A be a noncommutative Banach algebra. Suppose there exists a continuous linear Jordan derivation $D:A{\rightarrow}A$ such that $D^2(x)[D(x),x]{\in}rad(A)$ or $[D(x),x]D^2(x){\in}rad(A)$ for all $x{\in}A$. In this case, we show that $D(A){\subseteq}rad(A)$.

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References

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