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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
##### Keywords:
polynomials; $$C^*$$-algebras
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