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I'm having a hard time trying to understand a proof of the Principle of Local Reflexivity. I'm following the proofs from

1) Topics in Banach Space Theory (by Fernando Albiac, Nigel J. Kalton) 2) http://www.math.tamu.edu/~schlump/sofar.pdf (some notes from Professor Schlump)

The proof in 2) is basically the same as in 1) , but with further details. I don't quite get why Ker($S$) is contained in Ker($S_1$) . And I don't get why that implies that there is a $T$ such that $S_1 = TS$.

Pretty please, can someone enlight me ?

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    In future, try not to post on both sites at the same time. This can lead to duplicated effort, or give the impression that one has not thought much about which site is more appropriate2012-02-28

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