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

Éric Ricard (1) , Jean Roydor (2)

1 LMNO - Laboratoire de Mathématiques Nicolas Oresme
2 IMB - Institut de Mathématiques de Bordeaux

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.

Keywords: Homomorphisms of Fourier algebras; Algebras; Operator spaces

Domains: Mathematics [math]; Functional Analysis [math.FA]

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⟩