The inf-convolution between algebra and optimization. Applications to the Banach-Stone theorem.

Mohammed Bachir (1)

1 Equations d'evolution

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]

Mohammed Bachir. The inf-convolution between algebra and optimization. Applications to the Banach-Stone theorem.. 2015. ⟨hal-01164797⟩