Asymmetric free spaces and canonical asymmetrizations
dc.creator | Daniilidis, Aris | |
dc.creator | Sepulcre, Juan Matías | |
dc.creator | Venegas M., Francisco | |
dc.date.accessioned | 2021-12-16T20:24:40Z | |
dc.date.accessioned | 2022-01-27T22:46:36Z | |
dc.date.available | 2021-12-16T20:24:40Z | |
dc.date.available | 2022-01-27T22:46:36Z | |
dc.date.created | 2021-12-16T20:24:40Z | |
dc.date.issued | 2021 | |
dc.identifier | Studia Mathematica Volume 261 Issue 1 Page 55-102 Published 2021 | |
dc.identifier | 10.4064/sm200527-24-11 | |
dc.identifier | https://repositorio.uchile.cl/handle/2250/183278 | |
dc.identifier.uri | http://repositorioslatinoamericanos.uchile.cl/handle/2250/3319421 | |
dc.description.abstract | A construction analogous to that of Godefroy-Kalton for metric spaces allows one to embed isometrically, in a canonical way, every quasi-metric space (X, d) in an asymmetric normed space F-a (X, d) (its quasi-metric free space, also called asymmetric free space or semi-Lipschitz free space). The quasi-metric free space satisfies a universal property (linearization of semi-Lipschitz functions). The (conic) dual of F-a (X, d) coincides with the non-linear asymmetric dual of (X, d), that is, the space SLip(0)(X, d) of semiLipschitz functions on (X, d), vanishing at a base point. In particular, for the case of a metric space (X, D), the above construction yields its usual free space. On the other hand, every metric space (X, D) naturally inherits a canonical asymmetrization coming from its free space F(X). This gives rise to a quasi-metric space (X, D+) and an asymmetric free space F-a (X, D+) . The symmetrization of the latter is isomorphic to the original free space F(X). The results of this work are illustrated with explicit examples. | |
dc.language | en | |
dc.publisher | Polish Acad Sciences Inst Mathematics-IMPAN | |
dc.rights | http://creativecommons.org/licenses/by-nc-nd/3.0/us/ | |
dc.rights | Attribution-NonCommercial-NoDerivs 3.0 United States | |
dc.source | Studia Mathematica | |
dc.subject | Free space | |
dc.subject | Canonical asymmetrization | |
dc.subject | Semi-Lipschitz functions | |
dc.subject | Quasi-metric space | |
dc.title | Asymmetric free spaces and canonical asymmetrizations | |
dc.type | Artículos de revistas |