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
Contributor : Mohammed Bachir
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Submitted on : Thursday, October 2, 2014 - 10:40:02 PM
Last modification on : Thursday, May 2, 2019 - 4:50:10 PM
Mohammed Bachir. The inf-convolution as a law of monoid. An analogue to the Banach-Stone theorem.. Journal of Mathematical Analysis and Applications, Elsevier, 2014, 420 (1), pp.145-166. ⟨hal-01071027⟩
