Lipschitz compact operators

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Title: Lipschitz compact operators
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 Análisis Matemático
Keywords: Lipschitz operator | Strongly Lipschitz p-integral operator | Strongly Lipschitz p-nuclear operator | Free Banach space
Knowledge Area: Análisis Matemático
Issue Date: 15-Feb-2014
Publisher: Elsevier
Citation: Journal of Mathematical Analysis and Applications. 2014, Accepted Manuscript, Available online 15 February 2014. doi:10.1016/j.jmaa.2014.02.012
Abstract: We introduce the notion of Lipschitz compact (weakly compact, finite-rank, approximable) operators from a pointed metric space X into a Banach space E. We prove that every strongly Lipschitz p-nuclear operator is Lipschitz compact and every strongly Lipschitz p-integral operator is Lipschitz weakly compact. A theory of Lipschitz compact (weakly compact, finite-rank) operators which closely parallels the theory for linear operators is developed. In terms of the Lipschitz transpose map of a Lipschitz operator, we state Lipschitz versions of Schauder type theorems on the (weak) compactness of the adjoint of a (weakly) compact linear operator.
URI: http://hdl.handle.net/10045/35672
ISSN: 0022-247X (Print) | 1096-0813 (Online)
DOI: 10.1016/j.jmaa.2014.02.012
Language: eng
Type: info:eu-repo/semantics/article
Peer Review: si
Publisher version: http://dx.doi.org/10.1016/j.jmaa.2014.02.012
Appears in Collections:INV - CADAGL - Artículos de Revistas

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