Linearization of holomorphic Lipschitz functions
- Autores
- Aron, Richard; Dimant, Veronica Isabel; García Lirola, Luis C.; Maestre, Manuel
- Año de publicación
- 2024
- Idioma
- inglés
- Tipo de recurso
- artículo
- Estado
- versión publicada
- Descripción
- Let X and Y be complex Banach spaces with B_X denoting the open unit ball of X. This paper studies various aspects of the {em holomorphic Lipschitz space} $mathcal HL_0(B_X,Y), endowed with the Lipschitz norm. This space consists of the functions in the intersection of the sets Lip_0(B_X,Y) of Lipschitz mappings and $mathcal H^infty(B_X,Y) of bounded holomorphic mappings, from B_X to Y. Thanks to the Dixmier-Ng theorem, mathcal HL_0(B_X, mathbb C)$ is indeed a dual space, whose predual $mathcal G_0(B_X) shares linearization properties with both the Lipschitz-free space and Dineen-Mujica predual of $mathcal H^infty(B_X). We explore the similarities and differences between these spaces, and combine techniques to study the properties of the space of holomorphic Lipschitz functions. In particular, we get that mathcal G_0(B_X) contains a 1-complemented subspace isometric to and that mathcal G_0(X) has the (metric) approximation property whenever X has it. We also analyze when mathcal G_0(B_X) is a subspace of mathcal G_0(B_Y), and we obtain an analogue of Godefroy´s characterization of functionals with a unique norm preserving extension in the holomorphic Lipschitz context.
Fil: Aron, Richard. Kent State University; Estados Unidos
Fil: Dimant, Veronica Isabel. Universidad de San Andrés. Departamento de Matemáticas y Ciencias; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: García Lirola, Luis C.. Universidad de Zaragoza; España
Fil: Maestre, Manuel. Universidad de Valencia; España - Materia
-
Holomorphic function
Lipschitz function
Linearization
Symmetric regularity - Nivel de accesibilidad
- acceso abierto
- Condiciones de uso
- https://creativecommons.org/licenses/by/2.5/ar/
- Repositorio
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/255623
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Linearization of holomorphic Lipschitz functionsAron, RichardDimant, Veronica IsabelGarcía Lirola, Luis C.Maestre, ManuelHolomorphic functionLipschitz functionLinearizationSymmetric regularityhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Let X and Y be complex Banach spaces with B_X denoting the open unit ball of X. This paper studies various aspects of the {em holomorphic Lipschitz space} $mathcal HL_0(B_X,Y), endowed with the Lipschitz norm. This space consists of the functions in the intersection of the sets Lip_0(B_X,Y) of Lipschitz mappings and $mathcal H^infty(B_X,Y) of bounded holomorphic mappings, from B_X to Y. Thanks to the Dixmier-Ng theorem, mathcal HL_0(B_X, mathbb C)$ is indeed a dual space, whose predual $mathcal G_0(B_X) shares linearization properties with both the Lipschitz-free space and Dineen-Mujica predual of $mathcal H^infty(B_X). We explore the similarities and differences between these spaces, and combine techniques to study the properties of the space of holomorphic Lipschitz functions. In particular, we get that mathcal G_0(B_X) contains a 1-complemented subspace isometric to and that mathcal G_0(X) has the (metric) approximation property whenever X has it. We also analyze when mathcal G_0(B_X) is a subspace of mathcal G_0(B_Y), and we obtain an analogue of Godefroy´s characterization of functionals with a unique norm preserving extension in the holomorphic Lipschitz context.Fil: Aron, Richard. Kent State University; Estados UnidosFil: Dimant, Veronica Isabel. Universidad de San Andrés. Departamento de Matemáticas y Ciencias; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: García Lirola, Luis C.. Universidad de Zaragoza; EspañaFil: Maestre, Manuel. Universidad de Valencia; EspañaWiley VCH Verlag2024-05info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/255623Aron, Richard; Dimant, Veronica Isabel; García Lirola, Luis C.; Maestre, Manuel; Linearization of holomorphic Lipschitz functions; Wiley VCH Verlag; Mathematische Nachrichten; 297; 8; 5-2024; 3024-30510025-584XCONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://onlinelibrary.wiley.com/doi/10.1002/mana.202300527info:eu-repo/semantics/altIdentifier/doi/10.1002/mana.202300527info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T09:57:42Zoai:ri.conicet.gov.ar:11336/255623instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-29 09:57:42.838CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse |
dc.title.none.fl_str_mv |
Linearization of holomorphic Lipschitz functions |
title |
Linearization of holomorphic Lipschitz functions |
spellingShingle |
Linearization of holomorphic Lipschitz functions Aron, Richard Holomorphic function Lipschitz function Linearization Symmetric regularity |
title_short |
Linearization of holomorphic Lipschitz functions |
title_full |
Linearization of holomorphic Lipschitz functions |
title_fullStr |
Linearization of holomorphic Lipschitz functions |
title_full_unstemmed |
Linearization of holomorphic Lipschitz functions |
title_sort |
Linearization of holomorphic Lipschitz functions |
dc.creator.none.fl_str_mv |
Aron, Richard Dimant, Veronica Isabel García Lirola, Luis C. Maestre, Manuel |
author |
Aron, Richard |
author_facet |
Aron, Richard Dimant, Veronica Isabel García Lirola, Luis C. Maestre, Manuel |
author_role |
author |
author2 |
Dimant, Veronica Isabel García Lirola, Luis C. Maestre, Manuel |
author2_role |
author author author |
dc.subject.none.fl_str_mv |
Holomorphic function Lipschitz function Linearization Symmetric regularity |
topic |
Holomorphic function Lipschitz function Linearization Symmetric regularity |
purl_subject.fl_str_mv |
https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
dc.description.none.fl_txt_mv |
Let X and Y be complex Banach spaces with B_X denoting the open unit ball of X. This paper studies various aspects of the {em holomorphic Lipschitz space} $mathcal HL_0(B_X,Y), endowed with the Lipschitz norm. This space consists of the functions in the intersection of the sets Lip_0(B_X,Y) of Lipschitz mappings and $mathcal H^infty(B_X,Y) of bounded holomorphic mappings, from B_X to Y. Thanks to the Dixmier-Ng theorem, mathcal HL_0(B_X, mathbb C)$ is indeed a dual space, whose predual $mathcal G_0(B_X) shares linearization properties with both the Lipschitz-free space and Dineen-Mujica predual of $mathcal H^infty(B_X). We explore the similarities and differences between these spaces, and combine techniques to study the properties of the space of holomorphic Lipschitz functions. In particular, we get that mathcal G_0(B_X) contains a 1-complemented subspace isometric to and that mathcal G_0(X) has the (metric) approximation property whenever X has it. We also analyze when mathcal G_0(B_X) is a subspace of mathcal G_0(B_Y), and we obtain an analogue of Godefroy´s characterization of functionals with a unique norm preserving extension in the holomorphic Lipschitz context. Fil: Aron, Richard. Kent State University; Estados Unidos Fil: Dimant, Veronica Isabel. Universidad de San Andrés. Departamento de Matemáticas y Ciencias; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina Fil: García Lirola, Luis C.. Universidad de Zaragoza; España Fil: Maestre, Manuel. Universidad de Valencia; España |
description |
Let X and Y be complex Banach spaces with B_X denoting the open unit ball of X. This paper studies various aspects of the {em holomorphic Lipschitz space} $mathcal HL_0(B_X,Y), endowed with the Lipschitz norm. This space consists of the functions in the intersection of the sets Lip_0(B_X,Y) of Lipschitz mappings and $mathcal H^infty(B_X,Y) of bounded holomorphic mappings, from B_X to Y. Thanks to the Dixmier-Ng theorem, mathcal HL_0(B_X, mathbb C)$ is indeed a dual space, whose predual $mathcal G_0(B_X) shares linearization properties with both the Lipschitz-free space and Dineen-Mujica predual of $mathcal H^infty(B_X). We explore the similarities and differences between these spaces, and combine techniques to study the properties of the space of holomorphic Lipschitz functions. In particular, we get that mathcal G_0(B_X) contains a 1-complemented subspace isometric to and that mathcal G_0(X) has the (metric) approximation property whenever X has it. We also analyze when mathcal G_0(B_X) is a subspace of mathcal G_0(B_Y), and we obtain an analogue of Godefroy´s characterization of functionals with a unique norm preserving extension in the holomorphic Lipschitz context. |
publishDate |
2024 |
dc.date.none.fl_str_mv |
2024-05 |
dc.type.none.fl_str_mv |
info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion http://purl.org/coar/resource_type/c_6501 info:ar-repo/semantics/articulo |
format |
article |
status_str |
publishedVersion |
dc.identifier.none.fl_str_mv |
http://hdl.handle.net/11336/255623 Aron, Richard; Dimant, Veronica Isabel; García Lirola, Luis C.; Maestre, Manuel; Linearization of holomorphic Lipschitz functions; Wiley VCH Verlag; Mathematische Nachrichten; 297; 8; 5-2024; 3024-3051 0025-584X CONICET Digital CONICET |
url |
http://hdl.handle.net/11336/255623 |
identifier_str_mv |
Aron, Richard; Dimant, Veronica Isabel; García Lirola, Luis C.; Maestre, Manuel; Linearization of holomorphic Lipschitz functions; Wiley VCH Verlag; Mathematische Nachrichten; 297; 8; 5-2024; 3024-3051 0025-584X CONICET Digital CONICET |
dc.language.none.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
info:eu-repo/semantics/altIdentifier/url/https://onlinelibrary.wiley.com/doi/10.1002/mana.202300527 info:eu-repo/semantics/altIdentifier/doi/10.1002/mana.202300527 |
dc.rights.none.fl_str_mv |
info:eu-repo/semantics/openAccess https://creativecommons.org/licenses/by/2.5/ar/ |
eu_rights_str_mv |
openAccess |
rights_invalid_str_mv |
https://creativecommons.org/licenses/by/2.5/ar/ |
dc.format.none.fl_str_mv |
application/pdf application/pdf |
dc.publisher.none.fl_str_mv |
Wiley VCH Verlag |
publisher.none.fl_str_mv |
Wiley VCH Verlag |
dc.source.none.fl_str_mv |
reponame:CONICET Digital (CONICET) instname:Consejo Nacional de Investigaciones Científicas y Técnicas |
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CONICET Digital (CONICET) |
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CONICET Digital (CONICET) |
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Consejo Nacional de Investigaciones Científicas y Técnicas |
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CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas |
repository.mail.fl_str_mv |
dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar |
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