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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.


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Article Information

TitleRepresentation of isometric isomorphisms between monoids of Lipschitz functions
SourceMethods Funct. Anal. Topology, Vol. 23 (2017), no. 4, 309-319
MilestonesReceived 26/12/2016; Revised 24/04/2017
CopyrightThe 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


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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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