Non-linear new product A ∗ B − B ∗ A derivations on ∗-algebras
Abstract 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 ͨ...
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| Autores principales: | , |
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| Lenguaje: | English |
| Publicado: |
Universidad Católica del Norte, Departamento de Matemáticas
2020
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| Materias: | |
| Acceso en línea: | http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172020000200467 |
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| Sumario: | Abstract 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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