# Difference between revisions of "Talk:Banach space"

From Encyclopedia of Mathematics

Line 8: | Line 8: | ||

--[[User:Jjg|Jjg]] 01:31, 19 April 2012 (CEST) | --[[User:Jjg|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. [[User:Camillo.delellis|Camillo]] 13:52, 21 July 2012 (CEST) |

## Latest revision as of 11:52, 21 July 2012

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There is much in this article which is out of date.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

**How to Cite This Entry:**

Banach space.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Banach_space&oldid=27130