Nonlinear Triple Product $$A^{*}B + B^{*}A$$ for Derivations on $$\ast$$-Algebras
Vahid Darvish, Mojtaba Nouri, Mehran Razeghi
Abstract
Let $$\mathcal{A}$$ be a prime $$\ast$$ -algebra. In this paper, assuming that $$\Phi:\mathcal{A}\to\mathcal{A}$$ satisfies $$\Phi(A\diamond B \diamond C)=\Phi(A)\diamond B \diamond C+A\diamond\Phi(B) \diamond C+A \diamond B \diamond \Phi(C)$$ where $$A\diamond B = A^{*}B + B^{*}A$$ for all $$A,B\in\mathcal{A}$$ , we prove that $$\Phi$$ is additive an $$\ast$$ -derivation.
Topics & Concepts
DiamondMathematicsPrime (order theory)Triple productProduct (mathematics)Nonlinear systemCombinatoricsAlgebra over a fieldPure mathematicsPhysicsChemistryQuantum mechanicsGeometryOrganic chemistryAdvanced Topics in AlgebraAdvanced Operator Algebra ResearchAlgebraic structures and combinatorial models