Lipschitz compact operators
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Title: | Lipschitz compact operators |
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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 INV - GAM - Artículos de Revistas |
Files in This Item:
File | Description | Size | Format | |
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2014_Jimenez-Vargas_etal_JMAA.pdf | Accepted Manuscript (acceso abierto) | 281,85 kB | Adobe PDF | Open Preview |
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