The inf-convolution between algebra and optimization. Applications to the Banach-Stone theorem.
Abstract
This work generalize and extend results obtained recently in [2] from the Banach spaces framework to the groups framework. We study abstract classe of functions monoids for the inf-convolution struture and gives a complete description of the group of unit of such monoids. We then apply this results to obtain various versions of the Banach-Stone theorem for the inf-convolution struture in the group framework. We also give as consequence an algebraic proof of the Banach-Dieudonée theorem. Our techniques are based on a new optimization result.
Domains
Functional Analysis [math.FA]
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