Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
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JORDAN DERIVATIONS ON PRIME RINGS AND THEIR APPLICATIONS IN BANACH ALGEBRAS, II

  • Kim, Byung-Do (Department of Mathematics Gangneung-Wonju National University)
  • Received : 2013.11.08
  • Accepted : 2014.01.16
  • Published : 2014.02.15
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Abstract

The purpose of this paper is to prove that the noncommutative version of the Singer-Wermer Conjecture is affirmative under certain conditions. Let A be a noncommutative Banach algebra. We show that if there exists a continuous linear Jordan derivation D : A ${\rightarrow}$ A such that [D(x), x]$D(x)^3{\in}$ rad(A) for all $x{\in}A$, then D(A) ${\subseteq}$ rad(A).

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References

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