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Proyecciones (Antofagasta)
Print version ISSN 0716-0917
Abstract
TAGHAVI, A. and RAZEGHI, M.. Non-linear new product A ∗ B − B ∗ A derivations on ∗-algebras. Proyecciones (Antofagasta) [online]. 2020, vol.39, n.2, pp.467-479. ISSN 0716-0917. http://dx.doi.org/10.22199/issn.0717-6279-2020-02-0029.
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.
Keywords : New product derivation: Prime ∗-algebra; Additive map.
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