Abstract
In this paper, we proved that each nonlinear nonglobal semi-Jordan triple derivable mapping on a 2-torsion free triangular algebra is an additive derivation. As its application, we get the similar conclusion on a nest algebra or a 2-torsion free block upper triangular matrix algebra, respectively.
Highlights
A natural and very interesting problem that we are dealing with is studying certain conditions on an algebra such that each Jordan derivation (nonlinear Jordan derivable mapping) is a derivation.In the past few decades, many mathematicians studied this problem and obtained abundant results
For all X, Y, Z ∈ A, such a Δ is an additive derivation on a 2-torsion-free triangular algebra
In order to prove eorem 1, we introduce Lemmas 1–5 and prove that Lemmas 1–5 hold
Summary
A natural and very interesting problem that we are dealing with is studying certain conditions on an algebra such that each Jordan (triple) derivation (nonlinear Jordan (triple) derivable mapping) is a derivation.In the past few decades, many mathematicians studied this problem and obtained abundant results. For all X, Y, Z ∈ A, such a Δ is an additive derivation on a 2-torsion-free triangular algebra. We will discuss the nonlinear nonglobal semi-Jordan triple derivable mappings on triangular algebras and obtain one main result (see eorem 1).
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