# Difference between revisions of "Talk:Banach space"

From Encyclopedia of Mathematics

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− | + | Modifications made during TeXing | |

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+ | * 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+ | There is much in this article which is out of date.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. | ||

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

## Revision as of 19:38, 19 April 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There is much in this article which is out of date.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)

**How to Cite This Entry:**

Banach space.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Banach_space&oldid=24799