Abstract : In this article we study the operation of inf-convolution in a new direction. We prove that the inf-convolution gives a monoid structure to the space of convex $k$-Lipschitz and bounded from below real-valued functions on a Banach space $X$. Then we show that the structure of the space $X$ is completely determined by the structure of this monoid by establishing an analogue to the Banach-Stone theorem. Some applications will be given.
https://hal-paris1.archives-ouvertes.fr/hal-01071027
Contributeur : Mohammed Bachir
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Soumis le : jeudi 2 octobre 2014 - 22:40:02
Dernière modification le : lundi 27 novembre 2017 - 14:14:02
Mohammed Bachir. The inf-convolution as a law of monoid. An analogue to the Banach-Stone theorem.. Journal of Mathematical Analysis an Applications, 2014, 420 (1), pp.145-166. 〈hal-01071027〉
