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Orthogonally additive holomorphic functions of bounded type over C(K)
- Part of
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- Journal:
- Proceedings of the Edinburgh Mathematical Society / Volume 53 / Issue 3 / October 2010
- Published online by Cambridge University Press:
- 12 August 2010, pp. 609-618
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- Article
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It is known that all k-homogeneous orthogonally additive polynomials P over C(K) are of the form
Thus, x ↦ xk factors all orthogonally additive polynomials through some linear form μ. We show that no such linearization is possible without homogeneity. However, we also show that every orthogonally additive holomorphic function of bounded type f over C(K) is of the form
for some μ and holomorphic h : C (K) → L1(μ) of bounded type.
