Diffeomorphisms between spheres and hyperplanes in infinite-dimensional Banach spaces

We prove that for every infinite-dimensional Banach space X with a Frechet differentiable norm, the sphere S-X is diffeomorphic to each closed hyperplane in X. We also prove that every infinite-dimensional Banach space Y having a (not necessarily equivalent) C-p norm (with p is an element of N boole...

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Detalhes bibliográficos
Autor: Azagra Rueda, Daniel
Formato: artículo
Fecha de publicación:1997
País:España
Recursos:Universidad Complutense de Madrid (UCM)
Repositorio:Docta Complutense
Idioma:inglés
OAI Identifier:oai:docta.ucm.es:20.500.14352/57010
Acesso em linha:https://hdl.handle.net/20.500.14352/57010
Access Level:acceso abierto
Palavra-chave:517.986
Infinite-dimensional Banach space
Unit sphere
Hyperplane
Diffeomorphism
Funciones (Matemáticas)
1202 Análisis y Análisis Funcional
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spelling Diffeomorphisms between spheres and hyperplanes in infinite-dimensional Banach spacesAzagra Rueda, Daniel517.986Infinite-dimensional Banach spaceUnit sphereHyperplaneDiffeomorphismFunciones (Matemáticas)1202 Análisis y Análisis FuncionalWe prove that for every infinite-dimensional Banach space X with a Frechet differentiable norm, the sphere S-X is diffeomorphic to each closed hyperplane in X. We also prove that every infinite-dimensional Banach space Y having a (not necessarily equivalent) C-p norm (with p is an element of N boolean OR {infinity}) is C-p diffeomorphic to Y \ {0}.Polish Acad Sciencies Inst MathematicsUniversidad Complutense de Madrid19971997-01-0119971997-01-01journal articlehttp://purl.org/coar/resource_type/c_6501info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/20.500.14352/57010reponame:Docta Complutenseinstname:Universidad Complutense de Madrid (UCM)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccessoai:docta.ucm.es:20.500.14352/570102026-06-02T12:44:21Z
dc.title.none.fl_str_mv Diffeomorphisms between spheres and hyperplanes in infinite-dimensional Banach spaces
title Diffeomorphisms between spheres and hyperplanes in infinite-dimensional Banach spaces
spellingShingle Diffeomorphisms between spheres and hyperplanes in infinite-dimensional Banach spaces
Azagra Rueda, Daniel
517.986
Infinite-dimensional Banach space
Unit sphere
Hyperplane
Diffeomorphism
Funciones (Matemáticas)
1202 Análisis y Análisis Funcional
title_short Diffeomorphisms between spheres and hyperplanes in infinite-dimensional Banach spaces
title_full Diffeomorphisms between spheres and hyperplanes in infinite-dimensional Banach spaces
title_fullStr Diffeomorphisms between spheres and hyperplanes in infinite-dimensional Banach spaces
title_full_unstemmed Diffeomorphisms between spheres and hyperplanes in infinite-dimensional Banach spaces
title_sort Diffeomorphisms between spheres and hyperplanes in infinite-dimensional Banach spaces
dc.creator.none.fl_str_mv Azagra Rueda, Daniel
author Azagra Rueda, Daniel
author_facet Azagra Rueda, Daniel
author_role author
dc.contributor.none.fl_str_mv Universidad Complutense de Madrid
dc.subject.none.fl_str_mv 517.986
Infinite-dimensional Banach space
Unit sphere
Hyperplane
Diffeomorphism
Funciones (Matemáticas)
1202 Análisis y Análisis Funcional
topic 517.986
Infinite-dimensional Banach space
Unit sphere
Hyperplane
Diffeomorphism
Funciones (Matemáticas)
1202 Análisis y Análisis Funcional
description We prove that for every infinite-dimensional Banach space X with a Frechet differentiable norm, the sphere S-X is diffeomorphic to each closed hyperplane in X. We also prove that every infinite-dimensional Banach space Y having a (not necessarily equivalent) C-p norm (with p is an element of N boolean OR {infinity}) is C-p diffeomorphic to Y \ {0}.
publishDate 1997
dc.date.none.fl_str_mv 1997
1997-01-01
1997
1997-01-01
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/20.500.14352/57010
url https://hdl.handle.net/20.500.14352/57010
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Polish Acad Sciencies Inst Mathematics
publisher.none.fl_str_mv Polish Acad Sciencies Inst Mathematics
dc.source.none.fl_str_mv reponame:Docta Complutense
instname:Universidad Complutense de Madrid (UCM)
instname_str Universidad Complutense de Madrid (UCM)
reponame_str Docta Complutense
collection Docta Complutense
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,301603

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