Characterization of \(n\)-Jordan multipliers. (English) Zbl 1500.47055
Summary: Let \(A\) be a Banach algebra and \(X\) be a (Banach) \(A\)-bimodule. A linear map \(T : A \rightarrow X\) is called an \(n\)-Jordan multiplier if \(T(a^n) = aT(a^{n - 1})\) for all \(a \in A\). In this paper, among other things, we show that under special hypotheses every \((n + 1)\)-Jordan multiplier is an \(n\)-Jordan multiplier and vice versa.
MSC:
| 47B48 | Linear operators on Banach algebras |
| 46L05 | General theory of \(C^*\)-algebras |
| 46H25 | Normed modules and Banach modules, topological modules (if not placed in 13-XX or 16-XX) |
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