Representation of isometric isomorphisms between monoids of Lipschitz functions

Authors

  • M. Bachir </span>Laboratoire SAMM 4543, Universite Paris 1 Panth &acute; eon-Sorbonne, Centre P.M.F. 90 rue Tolbiac 75634 Paris cedex 13

DOI:

Keywords:

Groups and monoids, isomorphisms and isometries, inf-convolution, $1$-Lipschitz map, Banach-Stone theorem

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.

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Published

2017-12-25

Issue

Vol. 23 No. 4 (2017)

Section

Articles

How to Cite

Bachir, M. “Representation of Isometric Isomorphisms Between Monoids of Lipschitz Functions”. Methods of Functional Analysis and Topology, vol. 23, no. 4, Dec. 2017, pp. 309-1, https://zen.imath.kiev.ua/index.php/mfat/article/view/674.