Biduality and density in Lipschitz function spaces

Please use this identifier to cite or link to this item:
Información del item - Informació de l'item - Item information
Title: Biduality and density in Lipschitz function spaces
Authors: Jiménez Vargas, Antonio | Sepulcre, Juan Matias | Villegas Vallecillos, Moisés
Research Group/s: Curvas Alpha-Densas. Análisis y Geometría Local
Center, Department or Service: Universidad de Alicante. Departamento de Matemáticas
Keywords: Lipschitz function | Little Lipschitz function | Hölder function | Lipschitz-free Banach space
Knowledge Area: Análisis Matemático
Issue Date: 2017
Publisher: Mathematica Scandinavica
Citation: Mathematica Scandinavica. 2017, 121(1): 92-100. doi:10.7146/math.scand.a-25987
Abstract: For pointed compact metric spaces (X,d), we address the biduality problem as to when the space of Lipschitz functions Lip0(X,d) is isometrically isomorphic to the bidual of the space of little Lipschitz functions lip0(X,d), and show that this is the case whenever the closed unit ball of lip0(X,d) is dense in the closed unit ball of Lip0(X,d) with respect to the topology of pointwise convergence. Then we apply our density criterion to prove in an alternative way the real version of a classical result which asserts that Lip0(X,dα) is isometrically isomorphic to lip0(X,dα)∗∗ for any α∈(0,1).
Sponsor: This research was partially supported by MICINN under project MTM 2010-17687.
ISSN: 0025-5521 (Print) | 1903-1807 (Online)
DOI: 10.7146/math.scand.a-25987
Language: eng
Type: info:eu-repo/semantics/article
Rights: © Mathematica Scandinavica
Peer Review: si
Publisher version:
Appears in Collections:INV - CADAGL - Artículos de Revistas

Files in This Item:
Files in This Item:
File Description SizeFormat 
Thumbnail2017_Jimenez-Vargas_etal_MathScand_preprint.pdf989,12 kBAdobe PDFOpen Preview

Items in RUA are protected by copyright, with all rights reserved, unless otherwise indicated.