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Characterization of \(n\)-Jordan multipliers through zero products. (English) Zbl 07586605

Summary: Let \(A\) be a unital \(C^\ast\)-algebra and \(X\) be a unital Banach \(A\)-bimodule. In this paper, we characterize \(n\)-Jordan multipliers \(T:A\longrightarrow X\) through the action on zero product. We prove that each continuous linear mapping \(T\) from group algebra \(L^1(G)\) into unital Banach \(A\)-bimodule \(X\) which satisfies a related condition is an \(n\)-Jordan multiplier.

MSC:

47B47 Commutators, derivations, elementary operators, etc.
47B49 Transformers, preservers (linear operators on spaces of linear operators)
15A86 Linear preserver problems
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