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Orthogonally additive polynomials on \(C^*\)-algebras. (English) Zbl 1159.46035
The authors show that for every orthogonally additive scalar \(n\)-homogeneous polynomial \(P\) on a \(C^{\ast}\)-algebra \(A\) there exists a \(\varphi\) in \(A^{\ast}\) so that \(P(x)=\varphi(x^{n})\) for every \(x\) in \(A\). The vector-valued analogue is also obtained.

MSC:
46L05 General theory of \(C^*\)-algebras
46G25 (Spaces of) multilinear mappings, polynomials
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