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Journal Articles Journal of Functional Analysis Year : 2018

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.

Dates and versions

hal-01876526 , version 1 (18-09-2018)

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Cite

Éric Ricard, Jean Roydor. Almost contractive maps between $C^*$ -algebras with applications to Fourier algebras. Journal of Functional Analysis, 2018, 275 (1), pp.196 - 210. ⟨10.1016/j.jfa.2017.11.012⟩. ⟨hal-01876526⟩
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