Orthogonally additive polynomials on spaces of continuous functions
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2005
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Academic Press
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Pérez García, D. & Villanueva Díez, I. «Orthogonally Additive Polynomials on Spaces of Continuous Functions». Journal of Mathematical Analysis and Applications, vol. 306, n.o 1, junio de 2005, pp. 97-105. DOI.org (Crossref), https://doi.org/10.1016/j.jmaa.2004.12.036.
Abstract
We show that, for every orthogonally additive homogeneous polynomial P on a space of continuous functions C(K) with values in a Banach space Y, there exists a linear operator S : C(K) -> Y such that P(f) = S(f(n)). This is the C(K) version of a related result of Sundaresam for polynomials on L-p spaces.