Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4615886 | Journal of Mathematical Analysis and Applications | 2014 | 13 Pages |
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.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
A. Jiménez-Vargas, J.M. Sepulcre, Moisés Villegas-Vallecillos,