The inf-convolution as a law of monoid. An analogue to the Banach-Stone theorem. - Archive ouverte HAL Access content directly
Journal Articles Journal of Mathematical Analysis and Applications Year : 2014

The inf-convolution as a law of monoid. An analogue to the Banach-Stone theorem.

Mohammed Bachir
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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.

Dates and versions

hal-01071027 , version 1 (02-10-2014)

Identifiers

• HAL Id : hal-01071027 , version 1

Cite

Mohammed Bachir. The inf-convolution as a law of monoid. An analogue to the Banach-Stone theorem.. Journal of Mathematical Analysis and Applications, 2014, 420 (1), pp.145-166. ⟨hal-01071027⟩

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