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ISSN : 1226-0657

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Vol.16 No.2
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ON CONTINUOUS LINEAR JORDAN DERIVATIONS OF BANACH ALGEBRAS

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081
2009, v.16 no.2, pp.227-241
Park, Kyoo-Hong
Kim, Byung-Do
Park,, K. , & Kim,, B. (2009). ON CONTINUOUS LINEAR JORDAN DERIVATIONS OF BANACH ALGEBRAS. Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 16(2), 227-241.
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Abstract

Let A be a Banach algebra. Suppose there exists a continuous linear Jordan derivation D : A <TEX>$\rightarrow$</TEX> A such that <TEX>$[D(x),\;x]D(x)^2[D(x),\;x]\;{\in}\;rad(A)$</TEX> for all <TEX>$x\;{\in}\;A$</TEX>. Then we have D(A) <TEX>$\subseteq$</TEX> rad(A).

keywords
prime and semi prime ring, derivation, Jordan derivation, Banach algebra, (Jacobson) radical

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Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics

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