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Journal Articles Journal of Functional Analysis Year : 2018

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

Éric Ricard
Jean Roydor
• Function : Author

#### 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.

#### Domains

Mathematics [math] Functional Analysis [math.FA]

### Dates and versions

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

### Identifiers

• HAL Id : hal-01876526 , version 1
• DOI :

### 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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