Open Access

# Representation of isometric isomorphisms between monoids of Lipschitz functions

### 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.

### Article Information

 Title Representation of isometric isomorphisms between monoids of Lipschitz functions Source Methods Funct. Anal. Topology, Vol. 23 (2017), no. 4, 309-319 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},
URL = {http://mfat.imath.kiev.ua/article/?id=1001},
}

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