Nonlinear Left Bi-skew Lie Type Derivations on ∗-Algebras
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Authors: M. ASHRAF, MD A. MADNI AND M. R. MOZUMDER
DOI: 10.46793/KgJMat2610.1605A
Abstract:
Let ???? be a unital ∗-algebra over ℂ (the field of complex number). For any α,β ∈????, define α∘β = α∗β −β∗α. In this article, it is shown that a map ???? : ????→???? (need not be linear) satisfies ????(Pn(λ1,λ2,…,λn)) = ∑ i=1nPn(λ1,…,λi−1,????(λi),λi+1,…,λn) for all λ1,λ2,…,λn ∈???? if and only if ???? is an additive ∗-derivation. As applications, we apply our main result to various special classes of unital ∗-algebras, such as prime ∗-algebras, factor von Neumann algebras and von Neumann algebra with no central summands of type I1.
Keywords:
Additive ∗-derivation, ∗-algebras, left bi-skew Lie derivation, factor von Neumann algebra.
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