Talk:Banach space

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There is much in this article which is out of date.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.

--Jjg 01:31, 19 April 2012 (CEST)

I miss the notion of weak$^\star$ convergence (wanted to link it in Convergence of measures). Also, Weak topology exists: it would be nice to link it here. But that page is focused on a more general context (topological vector spaces) and it would be nice to make there a reference to Banach space theory. Camillo 13:52, 21 July 2012 (CEST)