Uploader: | Nejinn |

Date Added: | 10 September 2012 |

File Size: | 54.89 Mb |

Operating Systems: | Windows NT/2000/XP/2003/2003/7/8/10 MacOS 10/X |

Downloads: | 25881 |

Price: | Free* [*Free Regsitration Required] |

### Banach space - Wikipedia

Precisely, for every Banach space Xthe map. On every non-reflexive Epsace space Xthere exist continuous linear functionals that are not norm-attaining. They are important in different branches of analysis, Harmonic analysis and Partial differential equations among others. Find out more about the Kindle Personal Document Service.

For example, every convex continuous function on the unit ball B of a reflexive space attains its minimum at some point in B. When X has the approximation propertythis closure coincides with the space of compact operators on X. A normed space X is a Banach space if and only if each absolutely convergent series in X converges, [2].

If Z is another Banach space such banaxh there is an isometric isomorphism from X onto a dense subset of Zthen Z is isometrically isomorphic to Y.

To send this article to your Kindle, first ensure no-reply cambridge.

In other areas of analysisthe spaces under study are banaxh Banach spaces. Characterizing Hilbert Space Topology. This Banach space Y is the completion of the normed space X. This page was last edited on 11 Novemberat If X is infinite-dimensional, there exist linear maps which are not continuous.

## Banach space

Furthermore, just as Enflo's example, this space X is a "hand-made" space that fails to have the approximation property. Theory 2— There exists a canonical factorization of T as esapce.

List of Banach spaces. Further, by the open mapping theorem, if there is a bounded linear operator from the Banach space X onto the Banach space Ythen Y is reflexive.

### [] Espaces de Banach-Colmez et faisceaux coh\'erents sur la courbe de Fargues-Fontaine

If X and Y are normed spaces over the same ground field Kthe set of all continuous K -linear maps T: This was disproved by Gilles Pisier in Thus, the vector space B XY can be given the operator norm. Theory 3866 — This applies in particular to separable reflexive Banach spaces. Weak compactness of the unit ball provides a tool for finding solutions in reflexive spaces to certain optimization problems.

The normed space X is called reflexive when the natural map. If one of the two spaces X or Y is complete or reflexiveseparableetc.

This is a consequence of the Hahn—Banach theorem. Every normed space X can be isometrically baanch in a Banach space. The Schauder system is a basis in the space C [0, 1].

## Mathematics > Number Theory

Del and BenitezC. Conversely, when K 1 is not homeomorphic to K expacethe multiplicative Banach—Mazur distance between C K 1 and C K 2 must be greater than or equal to 2see above the results by Amir and Cambern.

Kadec's theorem was extended by Torunczyk, who proved [58] that any two Banach spaces are homeomorphic if and only if they have the same density characterthe minimum cardinality of a dense subset. A necessary and espave condition for the norm of a Banach space X to be associated to an inner product is the parallelogram identity:.

According to the Banach—Mazur theoremevery Banach space is isometrically isomorphic to a subspace of some C K. France 67—69 — espave, 23 —

In my opinion you are not right. I am assured. Let's discuss. Write to me in PM, we will communicate.

In it something is also idea good, agree with you.

I am sorry, that I interrupt you, but it is necessary for me little bit more information.

Choice at you hard

Please, more in detail