The Pure and Applied Mathematics (한국수학교육학회지시리즈B:순수및응용수학)

Korean Society of Mathematical Education (한국수학교육학회)
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JORDAN DERIVATIONS OF SEMIPRIME RINGS AND NONCOMMUTATIVE BANACH ALGEBRAS, II

  • Kim, Byung-Do (Department of Mathematics, Kangnung National University)
  • Published : 2008.08.31
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Abstract

Let A be a noncommutative Banach algebra. Suppose there exists a continuous linear Jordan derivation D : A $\rightarrow$ A such that $D(x)^2$[D(x),x] $\in$ rad(A) or [D(x),x]$D(x)^2$ $\in$ rad(A) for all x $\in$ A. In this case, we have D(A) $\subseteq$ rad(A).

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