Lipschitz free p-spaces for 0 < p < 1

This paper initiates the study of the structure of a new class of p-Banach spaces, 0 <p < 1, namely the Lipschitz free p-spaces (alternatively called Arens—Eells p-spaces) Fp(M) over p-metric spaces. We systematically develop the theory and show that some results hold as in the case of...

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Detalles Bibliográficos
Autores: Albiac Alesanco, Fernando José, Ansorena, José L., Cúth, Marek, Doucha, Michal
Tipo de recurso: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2020
País:España
Institución:Universidad Pública de Navarra
Repositorio:Academica-e. Repositorio Institucional de la Universidad Pública de Navarra
OAI Identifier:oai:academica-e.unavarra.es:2454/39430
Acceso en línea:https://hdl.handle.net/2454/39430
Access Level:acceso abierto
Palabra clave:p-Banach spaces
Lipschitz free p-spaces
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spelling Lipschitz free p-spaces for 0 < p < 1Albiac Alesanco, Fernando JoséAnsorena, José L.Cúth, MarekDoucha, Michalp-Banach spacesLipschitz free p-spacesThis paper initiates the study of the structure of a new class of p-Banach spaces, 0 <p < 1, namely the Lipschitz free p-spaces (alternatively called Arens—Eells p-spaces) Fp(M) over p-metric spaces. We systematically develop the theory and show that some results hold as in the case of p = 1, while some new interesting phenomena appear in the case 0 <p < 1 which have no analogue in the classical setting. For the former, we, e.g., show that the Lipschitz free p-space over a separable ultrametric space is isomorphic to ℓp for all 0 <p ≤ 1. On the other hand, solving a problem by the first author and N. Kalton, there are metric spaces N⊂M such that the natural embedding from Fp(N) to Fp(M) is not an isometry.F. Albiac acknowledges the support of the Spanish Ministry for Economy and Competitivity Grants MTM2014-53009-P for Análisis Vectorial, Multilineal y Aplicaciones, and MTM2016-76808-P for Operators, lattices, and structure of Banach spaces as well as the Spanish Ministry for Science and Innovation under Grant PID2019-1077701GB-I00. J. L. Ansorena acknowledges the support of the Spanish Ministry for Economy and Competitivity Grant MTM2014-53009-P for Análisis Vectorial, Multilineal y Aplicaciones. M. Cúth has been supported by Charles University Research program No. UNCE/SCI/023 and by the Research grant GACR 17-04197Y. M. Doucha was supported by the GACR project 16-34860L and RVO: 67985840.SpringerHebrew University Magnes PressEstatistika, Informatika eta MatematikaInstitute for Advanced Materials and Mathematics - INAMAT2Estadística, Informática y Matemáticas2020info:eu-repo/semantics/articleinfo:eu-repo/semantics/acceptedVersionapplication/pdfhttps://hdl.handle.net/2454/39430reponame:Academica-e. Repositorio Institucional de la Universidad Pública de Navarrainstname:Universidad Pública de NavarraInglésinfo:eu-repo/grantAgreement/MINECO//MTM2014-53009-Pinfo:eu-repo/grantAgreement/ES/1PE/MTM2016-76808-P© 2020, The Hebrew University of Jerusaleminfo:eu-repo/semantics/openAccessoai:academica-e.unavarra.es:2454/394302026-06-17T12:41:47Z
dc.title.none.fl_str_mv Lipschitz free p-spaces for 0 < p < 1
title Lipschitz free p-spaces for 0 < p < 1
spellingShingle Lipschitz free p-spaces for 0 < p < 1
Albiac Alesanco, Fernando José
p-Banach spaces
Lipschitz free p-spaces
title_short Lipschitz free p-spaces for 0 < p < 1
title_full Lipschitz free p-spaces for 0 < p < 1
title_fullStr Lipschitz free p-spaces for 0 < p < 1
title_full_unstemmed Lipschitz free p-spaces for 0 < p < 1
title_sort Lipschitz free p-spaces for 0 < p < 1
dc.creator.none.fl_str_mv Albiac Alesanco, Fernando José
Ansorena, José L.
Cúth, Marek
Doucha, Michal
author Albiac Alesanco, Fernando José
author_facet Albiac Alesanco, Fernando José
Ansorena, José L.
Cúth, Marek
Doucha, Michal
author_role author
author2 Ansorena, José L.
Cúth, Marek
Doucha, Michal
author2_role author
author
author
dc.contributor.none.fl_str_mv Estatistika, Informatika eta Matematika
Institute for Advanced Materials and Mathematics - INAMAT2
Estadística, Informática y Matemáticas
dc.subject.none.fl_str_mv p-Banach spaces
Lipschitz free p-spaces
topic p-Banach spaces
Lipschitz free p-spaces
description This paper initiates the study of the structure of a new class of p-Banach spaces, 0 <p < 1, namely the Lipschitz free p-spaces (alternatively called Arens—Eells p-spaces) Fp(M) over p-metric spaces. We systematically develop the theory and show that some results hold as in the case of p = 1, while some new interesting phenomena appear in the case 0 <p < 1 which have no analogue in the classical setting. For the former, we, e.g., show that the Lipschitz free p-space over a separable ultrametric space is isomorphic to ℓp for all 0 <p ≤ 1. On the other hand, solving a problem by the first author and N. Kalton, there are metric spaces N⊂M such that the natural embedding from Fp(N) to Fp(M) is not an isometry.
publishDate 2020
dc.date.none.fl_str_mv 2020
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/acceptedVersion
format article
status_str acceptedVersion
dc.identifier.none.fl_str_mv https://hdl.handle.net/2454/39430
url https://hdl.handle.net/2454/39430
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv info:eu-repo/grantAgreement/MINECO//MTM2014-53009-P
info:eu-repo/grantAgreement/ES/1PE/MTM2016-76808-P
dc.rights.none.fl_str_mv © 2020, The Hebrew University of Jerusalem
info:eu-repo/semantics/openAccess
rights_invalid_str_mv © 2020, The Hebrew University of Jerusalem
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Springer
Hebrew University Magnes Press
publisher.none.fl_str_mv Springer
Hebrew University Magnes Press
dc.source.none.fl_str_mv reponame:Academica-e. Repositorio Institucional de la Universidad Pública de Navarra
instname:Universidad Pública de Navarra
instname_str Universidad Pública de Navarra
reponame_str Academica-e. Repositorio Institucional de la Universidad Pública de Navarra
collection Academica-e. Repositorio Institucional de la Universidad Pública de Navarra
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15.300719

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