Abstract : We prove that unital almost contractive maps between ⁎-algebras enjoy approximately certain properties of unital positive maps (such as selfadjointness or the Kadison–Schwarz inequality). Our main application is a description of almost contractive homomorphisms between Fourier algebras and Fourier–Stieltjes algebras: they are actually contractive if their norm is smaller than 1.00018. For surjective isomorphisms of Fourier algebras, the bound 1.0005 is sufficient in order to obtain an isometry.
https://hal-normandie-univ.archives-ouvertes.fr/hal-01876526 Contributor : Éric RicardConnect in order to contact the contributor Submitted on : Tuesday, September 18, 2018 - 3:04:06 PM Last modification on : Saturday, December 4, 2021 - 3:43:20 AM
Éric Ricard, Jean Roydor. Almost contractive maps between $C^*$ -algebras with applications to Fourier algebras. Journal of Functional Analysis, Elsevier, 2018, 275 (1), pp.196 - 210. ⟨10.1016/j.jfa.2017.11.012⟩. ⟨hal-01876526⟩