Linear Generalized n -Derivations on C ∗ -Algebras

Shakir Ali (), Amal S. Alali and Vaishali Varshney
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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

Mathematics, 2024, vol. 12, issue 10, 1-11

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.

Keywords: linear derivation; generalized n -derivation; Lie ideal; Banach algebra; C ? -algebra (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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