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Almost contractive maps between $C^*$ -algebras with applications to Fourier algebras

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.
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Submitted on : Tuesday, September 18, 2018 - 3:04:06 PM
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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⟩



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