Representation of vector valued nonlinear functions

Mizel, Victor J.; Sundaresan, K.

doi:10.1090/S0002-9947-1971-0279647-8

Representation of vector valued nonlinear functions
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by Victor J. Mizel and K. Sundaresan

Trans. Amer. Math. Soc. 159 (1971), 111-127

DOI: https://doi.org/10.1090/S0002-9947-1971-0279647-8

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Abstract:

A representation theorem for “additive” nonlinear functional on spaces ${L^p}(\mu )$ is here extended to “additive” nonlinear functions from Lebesgue-Bochner function spaces $L_E^p(\mu )$ ($E$ a separable Banach space) into Banach spaces $B$. A counterexample is provided to show that the restriction to separable $E$ is essential.

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