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

Éric Ricard; Jean Roydor

doi:10.1016/j.jfa.2017.11.012

Journal articles

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

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.

Keywords : Homomorphisms of Fourier algebras Algebras Operator spaces

Document type :

Journal articles

Domain :

Mathematics [math] / Functional Analysis [math.FA]

Complete list of metadatas

https://hal-normandie-univ.archives-ouvertes.fr/hal-01876526
Contributor : Éric Ricard <>
Submitted on : Tuesday, September 18, 2018 - 3:04:06 PM
Last modification on : Monday, April 27, 2020 - 4:14:03 PM

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

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

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