Non-linear new product A*B-B*A derivations on *-algebras
DOI:
https://doi.org/10.22199/issn.0717-6279-2020-02-0029Keywords:
New product derivation, Prime ∗-algebra, Additive mapAbstract
Let A be a prime ∗-algebra with unit I and a nontrivial projection. Then the map Φ : A → A satisfies in the following condition
Φ(A ⋄ B) = Φ(A) ⋄ B + A ⋄ Φ(B)
where A⋄ B = A∗B −B∗A for all A, B ∈ A, is additive. Moreover, if Φ(αI) is self-adjoint operator for α ∈ {1, i} then Φ is a ∗-derivation.
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