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For my quetion in MO is $\forall X$, $X^{**}$=X$\oplus Y$ for a $Y$ another set I am not really sure in Thomas answer why the first assumption saying that such a $Y$ exist iff the sequence $0 \to X \to \varphi(X^∗)^∗ \to \eta \mathrm{coker}\varphi \to 0$ splits?

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    Would you please give me a reference or a more detailed explanation on why such a$Y$exist iff the sequence 0→X→φ(X∗)∗→ηcokerφ→0 splits?2012-11-13

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