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Modifications made during TeXing

* in the definition of the quotient norm : added missing subscript to LHS ($Y$ becomes $Y_1$)
* in relationship relating the convexity modulus of a Banach space $X$ and the smoothness modulus of $X^*$ : replaced $\epsilon(\tau)$ by $\epsilon\tau$, since the former suggests a non-existent functional dependance (see, for example, Lemma 9.8 of Banach Space Theory: The Basis for Linear and Nonlinear Analysis By Marián Fabian, Petr Habala, Petr Hajek, Vicente Montesinos, Václav Zizler.
* in equation (*) : added missing subscript ($x\in X$ becomes $x_k\in X$)

There is much in this article which is out of date. Most of the open questions mentioned are no longer open (mostly due to Gowers) but I leave it to a Banach-space expert to make the required modifications.

--[[User:Jjg|Jjg]] 01:31, 19 April 2012 (CEST)