학술저널
JORDAN DERIVATIONS ON SEMIPRIME RINGS AND THEIR RADICAL RANGE IN BANACH ALGEBRAS
- 충청수학회
- Journal of the Chungcheong Mathematical Society
- Volume 31, No. 1
-
2018.021 - 12 (12 pages)
- 13
Let R be a 3!-torsion free noncommutative semiprime ring, and suppose there exists a Jordan derivation D : R → R such that D 2 (x)[D(x), x] = 0 or [D(x), x]D 2 (x) = 0 for all x ∈ R. In this case we have f (x) 5 = 0 for all x ∈ R. Let A be a noncommutative Banach algebra. Suppose there exists a continuous linear Jordan derivation D : A → A such that D 2 (x)[D(x), x] ∈ rad(A) or [D(x), x]D 2 (x) ∈ rad(A) for all x ∈ A. In this case, we show that D(A) ⊆ rad(A).
1. Introduction
2. Preliminaries
3. Main theorems
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