Let E, F be Banach spaces. In the case that F is reflexive we give a description
for the solutions (f, g) of the Banach-orthogonality equation
f(x), g(α) = x, α ∀x ∈ E, ∀α ∈ E∗,
where f : E → F, g : E∗ → F ∗ are two maps. Our result generalizes the recent result of
Lukasik and W´  ojcik in the case that E and F are Hilbert spaces.

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• Decomposition of functions between Banach spaces in the orthogonality equation