About: Auxiliary normed space

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In functional analysis, two methods of constructing normed spaces from disks were systematically employed by Alexander Grothendieck to define nuclear operators and nuclear spaces. One method is used if the disk is bounded: in this case, the auxiliary normed space is with norm The other method is used if the disk is absorbing: in this case, the auxiliary normed space is the quotient space If the disk is both bounded and absorbing then the two auxiliary normed spaces are canonically isomorphic (as topological vector spaces and as normed spaces).

Attributes	Values
rdfs:label	Auxiliary normed space (en)
rdfs:comment	In functional analysis, two methods of constructing normed spaces from disks were systematically employed by Alexander Grothendieck to define nuclear operators and nuclear spaces. One method is used if the disk is bounded: in this case, the auxiliary normed space is with norm The other method is used if the disk is absorbing: in this case, the auxiliary normed space is the quotient space If the disk is both bounded and absorbing then the two auxiliary normed spaces are canonically isomorphic (as topological vector spaces and as normed spaces). (en)
name	Theorem (en)
dcterms:subject	Functional analysis
Wikipage page ID	63622954 (xsd:integer)
Wikipage revision ID	1100721282 (xsd:integer)
Link from a Wikipage to another Wikipage	Bounded set (topological vector space) Convex set Norm (mathematics) Nuclear operator Nuclear space Fréchet space Minkowski functional Locally convex topological vector space Functional analysis Polar set Balanced set Banach space Topological vector space Topological vector spaces Hausdorff space Linear span Absolutely convex set Alexander Grothendieck Normed space Quotient space (linear algebra) Radial set Absorbing set Functional analysis Bipolar theorem Bornivorous set Metrizable topological vector space Seminorm Subspace topology Sequentially complete Normed vector space Mackey convergent sequence Quotient map Quotient topology Seminormed space Von Neumann bounded
Link from a Wikipage to an external page	https://ncatlab.org/nlab/show/nuclear+space
sameAs	Auxiliary normed space Auxiliary normed space
dbp:wikiPageUsesTemplate	dbt:Grothendieck_Produits_Tensoriels_Topologiques_et_Espaces_Nucléaires dbt:Annotated_link dbt:Em dbt:More_footnotes dbt:Reflist dbt:Sfn dbt:Math_proof dbt:Diestel_The_Metric_Theory_of_Tensor_Products_Grothendieck's_Résumé_Revisited dbt:Functional_analysis dbt:Hogbe-Nlend_Bornologies_and_Functional_Analysis dbt:Hogbe-Nlend_Moscatelli_Nuclear_and_Conuclear_Spaces dbt:Husain_Khaleelulla_Barrelledness_in_Topological_and_Ordered_Vector_Spaces dbt:Khaleelulla_Counterexamples_in_Topological_Vector_Spaces dbt:Math_theorem dbt:Narici_Beckenstein_Topological_Vector_Spaces dbt:Pietsch_Nuclear_Locally_Convex_Spaces dbt:Robertson_Topological_Vector_Spaces dbt:Ryan_Introduction_to_Tensor_Products_of_Banach_Spaces dbt:Schaefer_Wolff_Topological_Vector_Spaces dbt:Trèves_François_Topological_vector_spaces,_distributions_and_kernels dbt:Wong_Schwartz_Spaces,_Nuclear_Spaces,_and_Tensor_Products dbt:Dubinsky_The_Structure_of_Nuclear_Fréchet_Spaces dbt:TopologicalTensorProductsAndNuclearSpaces
has abstract	In functional analysis, two methods of constructing normed spaces from disks were systematically employed by Alexander Grothendieck to define nuclear operators and nuclear spaces. One method is used if the disk is bounded: in this case, the auxiliary normed space is with norm The other method is used if the disk is absorbing: in this case, the auxiliary normed space is the quotient space If the disk is both bounded and absorbing then the two auxiliary normed spaces are canonically isomorphic (as topological vector spaces and as normed spaces). (en)
math statement	If is a disk in a topological vector space then is bounded in if and only if the inclusion map is continuous. (en) Let be a disk in a vector space If there exists a Hausdorff TVS topology on such that is a bounded sequentially complete subset of then is a Banach space. (en)
prov:wasDerivedFrom	wikipedia-en:Auxiliary_normed_space?oldid=1100721282&ns=0
page length (characters) of wiki page	26530 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Auxiliary_normed_space
is Link from a Wikipage to another Wikipage of	Nuclear space Locally convex topological vector space Auxiliary normed spaces Balanced set Absorbing set Bornivorous set Polar topology Metrizable topological vector space List of things named after Stefan Banach Fast convergence Fast convergent sequence Katowice property Infracomplete Infracomplete space Banach disk Bounded completant
is Wikipage redirect of	Auxiliary normed spaces Fast convergence Fast convergent sequence Katowice property Infracomplete Infracomplete space Banach disk Bounded completant
is foaf:primaryTopic of	wikipedia-en:Auxiliary_normed_space

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