Abstract
We prove that each isometric isomorphism between the monoids of all nonnegative $1$-Lipschitz maps defined on invariant metric groups and equipped with the inf-convolution law, is given canonically from an isometric isomorphism between their groups of units.
Key words: Groups and monoids, isomorphisms and isometries, inf-convolution, $1$-Lipschitz map, Banach-Stone theorem.
Full Text
Article Information
| Title | Representation of isometric isomorphisms between monoids of Lipschitz functions |
| Source | Methods Funct. Anal. Topology, Vol. 23 (2017), no. 4, 309-319 |
| MathSciNet |
MR3745184 |
| Milestones | Received 26/12/2016; Revised 24/04/2017 |
| Copyright | The Author(s) 2017 (CC BY-SA) |
Authors Information
Mohammed Bachir
Laboratoire SAMM 4543, Universite Paris 1 Panth ´ eon-Sorbonne, Centre P.M.F. 90 rue Tolbiac 75634 Paris cedex 13
Citation Example
Mohammed Bachir, Representation of isometric isomorphisms between monoids of Lipschitz functions, Methods Funct. Anal. Topology 23
(2017), no. 4, 309-319.
BibTex
@article {MFAT1001,
AUTHOR = {Mohammed Bachir},
TITLE = {Representation of isometric isomorphisms between monoids of Lipschitz functions},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {23},
YEAR = {2017},
NUMBER = {4},
PAGES = {309-319},
ISSN = {1029-3531},
MRNUMBER = {MR3745184},
URL = {http://mfat.imath.kiev.ua/article/?id=1001},
}
