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In this note, we obtain range inclusion results for left Jordan derivations on Banach algebras: (i) Let δ be a spectrally bounded left Jordan derivation on a Banach algebra А. Then δ maps Аinto its Jacobson radical. (ii) Let δ be a left Jordan derivation on a unital Banach algebra А with the condition sup$\{r(c-1δ(c)): c ∈ A invertible} < ∞. Then δ maps А into its Jacobson radical.
Moreover, we give an exact answer to the conjecture raised by Ashraf and Ali in \cite[p.\,260]{Ash08}: every generalized left Jordan derivation on 2-torsion free semiprime rings is a generalized left derivation.
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참고문헌 (20)
참고문헌 신청
B. Zalar / 1991 / On centralizers of semiprime rings / Comment. Math. Univ. Carolin. 32 (4) : 609 ~ 614
F. F. Bonsall / 1973 / Complete Normed Algebras. in: Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 80 / Springer-Verlag
I. M. Singer / 1955 / Derivations on commutative normed algebras / Math. Ann. 129 : 260 ~ 264
J. Vukman / 1997 / Jordan left derivations on semiprime rings / Math. J. Okayama Univ. 39 : 1 ~ 6
J. Vukman / 2007 / A note on generalized derivations of semiprime rings / Taiwanese J. Math. 11 (2) : 367 ~ 370
F. F. Bonsall / 1973 / Complete Normed Algebras. in: Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 80 / Springer-Verlag
I. M. Singer / 1955 / Derivations on commutative normed algebras / Math. Ann. 129 : 260 ~ 264
J. Vukman / 1997 / Jordan left derivations on semiprime rings / Math. J. Okayama Univ. 39 : 1 ~ 6
J. Vukman / 2007 / A note on generalized derivations of semiprime rings / Taiwanese J. Math. 11 (2) : 367 ~ 370
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