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Linear Generalized n -Derivations on C ∗ -Algebras

Author

Listed:
  • Shakir Ali

    (Department of Mathematics, Faculty of Science, Aligarh Muslim University, Aligarh 202002, India)

  • Amal S. Alali

    (Department of Mathematical Sciences, College of Science, Princess Nourah Bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia)

  • Vaishali Varshney

    (Department of Mathematics, Faculty of Science, Aligarh Muslim University, Aligarh 202002, India)

Abstract

Let n ≥ 2 be a fixed integer and A be a C ∗ -algebra. A permuting n -linear map G : A n → A is known to be symmetric generalized n -derivation if there exists a symmetric n -derivation D : A n → A such that G ς 1 , ς 2 , … , ς i ς i ′ , … , ς n = G ς 1 , ς 2 , … , ς i , … , ς n ς i ′ + ς i D ( ς 1 , ς 2 , … , ς i ′ , … , ς n ) holds ∀ ς i , ς i ′ ∈ A . In this paper, we investigate the structure of C ∗ -algebras involving generalized linear n -derivations. Moreover, we describe the forms of traces of linear n -derivations satisfying certain functional identity.

Suggested Citation

  • Shakir Ali & Amal S. Alali & Vaishali Varshney, 2024. "Linear Generalized n -Derivations on C ∗ -Algebras," Mathematics, MDPI, vol. 12(10), pages 1-11, May.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:10:p:1558-:d:1396128
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    References listed on IDEAS

    as
    1. Xinfeng Liang & Ji Gao, 2021. "Generalized Jordan N-Derivations of Unital Algebras with Idempotents," Journal of Mathematics, Hindawi, vol. 2021, pages 1-5, June.
    2. Mohamad Nagy Daif & Howard E. Bell, 1992. "Remarks on derivations on semiprime rings," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 15, pages 1-2, January.
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