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December 2, 2025Axioms4 citationsOpen Access

Nonlinear Mixed Jordan-Type Derivations on ∗-Algebra

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MMMuzibur Rahman Mozumder

Key Points

  • Additive ∗-derivation properties revealed for nonlinear mixed bi-skew Jordan n-derivations under specified conditions.
  • Main finding applies to significant classes of ∗-algebras like prime and von Neumann algebra.
  • Observational analysis across different types of ∗-algebras demonstrates the versatility of the new derivation types.
  • Highlights the importance of understanding derivations in the framework of von Neumann algebra.

Abstract

Let A be a unital ∗-algebra over the complex fields C. In this article, it is proved that a nonlinear mixed bi-skew Jordan n-derivation is an additive ∗-derivation under certain conditions. As applications, the main result is applied to some special classes of ∗-algebras such as prime ∗-algebra, standard operator algebra, factor von Neumann algebra and von Neumann algebra with no central summands of type I1.

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Muzibur Rahman Mozumder (2025) studied this question.

synapsesocial.com/papers/692e3d8d6c9b3ab28c1875d6https://doi.org/10.3390/axioms14120874
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Also Consider

Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context:

  1. 1A note on nonlinear mixed Jordan triple derivation on *-algebras2022 · 19 citations
  2. 2Nonlinear bi-skew Jordan-type derivations on factor von Neumann algebras2023 · 18 citations
  3. 3The Second Nonlinear Mixed Jordan Triple Derivable Mapping on Factor von Neumann Algebras2021 · 19 citations
  4. 4Nonlinear *-Jordan-type derivations on *-algebras2021 · 30 citations
  5. 5Multiplicative bi-skew Jordan triple derivations on prime ∗-algebra2023 · 18 citations