| dbo:description
|
- typ przestrzeni w matematyce (pl)
- ruang vektor dengan metrik yang memungkinkan penghitungan panjang vektor dan jarak antara vektor dan lengkap dalam arti bahwa urutan Cauchy vektor selalu konvergen ke batas yang didefinisikan dengan baik yang ada di dalam ruang (in)
- espacio vectorial completo normado (es)
- espai vectorial complet (ca)
- espazo vectorial normado completo (gl)
- normed vector space that is complete (en)
- normirani vektorski prostor, ki je poln (sl)
- spaČiu vectorial normat complet (ro)
- vektora spaco kun kompleta nomro (eo)
- vollständiger, normierter Vektorraum (de)
- vektoriavaruus, jossa jokainen Cauchyn jono suppenee (matematiikka) (fi)
- пОНнОо нОŃПиŃОваннОо вокŃĐžŃнОо ĐżŃĐžŃŃŃĐ°Đ˝ŃŃвО (ru)
- espace vectoriel normĂŠ sur un corps de nombres et complet pour la norme (fr)
- ăăŤă äťăăăăçˇĺ犺éă§ăăŁăŚăăăŽăăŤă ăĺŽăăčˇé˘ć§é ăĺŽĺă§ăăă㎠(ja)
|
| dbo:thumbnail
| |
| dbo:wikiPageExternalLink
| |
| dbo:wikiPageWikiLink
| |
| dbp:id
| |
| dbp:mathStatement
|
- Let be a linear mapping between Banach spaces. The graph of is closed in if and only if is continuous. (en)
- If a Banach space is the internal direct sum of closed subspaces then is isomorphic to (en)
- Let be a normed vector space. Then the closed unit ball of the dual space is compact in the weak* topology. (en)
- If and are compact Hausdorff spaces and if and are isometrically isomorphic, then the topological spaces and are homeomorphic. (en)
- For every measure the space is weakly sequentially complete. (en)
- Let be a separable Banach space. The following are equivalent:
*The space does not contain a closed subspace isomorphic to
*Every element of the bidual is the weak*-limit of a sequence in (en)
- A Banach space isomorphic to all its infinite-dimensional closed subspaces is isomorphic to a separable Hilbert space. (en)
- for all (en)
- Let be a normed space. If is separable, then is separable. (en)
- Suppose that and are Banach spaces and that Suppose further that the range of is closed in Then is isomorphic to (en)
- Let be a bounded sequence in a Banach space. Either has a weakly Cauchy subsequence, or it admits a subsequence equivalent to the standard unit vector basis of (en)
- Let be a Banach space and be a normed vector space. Suppose that is a collection of continuous linear operators from to The uniform boundedness principle states that if for all in we have then (en)
- Let be an uncountable compact metric space. Then is isomorphic to (en)
- Let be a vector space over the field Let further
* be a linear subspace,
* be a sublinear function and
* be a linear functional so that for all
Then, there exists a linear functional so that (en)
- For a Banach space the following two properties are equivalent:
* is reflexive.
* for all in there exists with so that (en)
- A set in a Banach space is relatively weakly compact if and only if every sequence in has a weakly convergent subsequence. (en)
- Every one-to-one bounded linear operator from a Banach space onto a Banach space is an isomorphism. (en)
- Let and be Banach spaces and be a surjective continuous linear operator, then is an open map. (en)
- Let be a reflexive Banach space. Then is separable if and only if is separable. (en)
|
| dbp:name
| |
| dbp:title
| |
| dbp:wikiPageUsesTemplate
| |
| dct:subject
| |
| gold:hypernym
| |
| rdf:type
| |
| rdfs:label
|
- Banach space (en)
- BanachĹŻv prostor (cs)
- Espai de Banach (ca)
- ΧĎĎÎżĎ ÎĎÎŹÎ˝ÎąĎ (el)
- Ů؜اإ باŮا؎ (ar)
- BanaÄĽa spaco (eo)
- Espacio de Banach (es)
- Espace de Banach (fr)
- Banachraum (de)
- Ruang Banach (in)
- Spazio di Banach (it)
- ăăăă犺é (ja)
- ë°ëí ęłľę° (ko)
- Banachruimte (nl)
- Espaço de Banach (pt)
- PrzestrzeĹ Banacha (pl)
- ĐанаŃ
Ńв ĐżŃĐžŃŃŃŃ (uk)
- Banachrum (sv)
- ĐанаŃ
ОвО ĐżŃĐžŃŃŃĐ°Đ˝ŃŃвО (ru)
- 塴ćżčľŤçŠşé´ (zh)
|
| rdfs:seeAlso
| |
| owl:sameAs
| |
| prov:wasDerivedFrom
| |
| foaf:depiction
| |
| foaf:isPrimaryTopicOf
| |
| is dbo:academicDiscipline
of | |
| is dbo:knownFor
of | |
| is dbo:wikiPageDisambiguates
of | |
| is dbo:wikiPageRedirects
of | |
| is dbo:wikiPageWikiLink
of | |
| is dbp:knownFor
of | |
| is rdfs:seeAlso
of | |
| is foaf:primaryTopic
of | |
