Abstract
Let n≥2 be a fixed integer and A be a C∗-algebra. A permuting n-linear map G:An→A is known to be symmetric generalized n-derivation if there exists a symmetric n-derivation D:An→A such that Gς1,ς2,…,ςiςi′,…,ςn=Gς1,ς2,…,ςi,…,ςnςi′+ςiD(ς1,ς2,…,ςi′,…,ςn) holds ∀ςi,ςi′∈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.
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