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- Jun 20, 2014

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Prove the following theorem of Tate: If $\phi : X\to Y$ is a mapping of real Banach spaces such that for some positive number $M$, $\lvert \phi(x + y) - \phi(x) - \phi(y)\rvert \le M$ ($x,y\in X$), then there is a unique additive mapping $\psi : X \to Y$ such that $\psi - \phi$ is bounded on $X$.

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