Question: Let Hf (c) be a bounding hyperplane of a subspace Z of a normed linear space X, that is, f (x) c for every

Let Hf (c) be a bounding hyperplane of a subspace Z of a normed linear space X, that is, f (x) ≤ c for every x ∈ Z. Then Z is contained in the kernel of f, that is,
f (x) = 0 for every x ∈ Z

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