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ISSN : 1226-0657

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Vol.15 No.2
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JORDAN DERIVATIONS OF SEMIPRIME RINGS AND NONCOMMUTATIVE BANACH ALGEBRAS, I

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
2008, v.15 no.2, pp.179-201
Kim, Byung-Do
Kim,, B. (2008). JORDAN DERIVATIONS OF SEMIPRIME RINGS AND NONCOMMUTATIVE BANACH ALGEBRAS, I. Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 15(2), 179-201.
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Abstract

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

keywords
semiprime ring, noncommutative Banach algebra, Jacobson radical, spectral radius, Jordan drivation

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

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