Rendiconti del Seminario Matematico della Università di Padova


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Volume 122, 2009, pp. 171–190
DOI: 10.4171/RSMUP/122-11

Generalized Derivations on (Semi-)Prime Rings and Noncommutative Banach Algebras

Feng Wei[1] and Zhankui Xiao[2]

(1) Department of Applied Mathematics, Beijing Institute of Technology, 100081, Beijing, China
(2) Department of Applied Mathematics, Beijing Institute of Technology, 100081, Beijing, China

We first give several polynomial identities of semiprime rings which make the additive mappings appearing in the identities to be generalized derivations. Then we study pairs of generalized Jordan derivations on prime rings. Let m,n be fixed positive integers, R be a noncommutative 2(m+n)!-torsion free prime ring with the center Z and μ, ν be a pair of generalized Jordan derivations on RR. If μ(xm)xn+ xnν(xm) ∈ Z for all xR, then μ and ν are left (or right) multipliers. In particular, if μ, ν are a pair of derivations on R satisfying the same assumption, then μ = ν = 0. Then applying these purely algebraic result we obtain several range inclusion results of pair of derivations on Banach algebras.

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Wei Feng, Xiao Zhankui: Generalized Derivations on (Semi-)Prime Rings and Noncommutative Banach Algebras. Rend. Sem. Mat. Univ. Padova 122 (2009), 171-190. doi: 10.4171/RSMUP/122-11