Spectrally bounded operators on simple 𝐶*-algebras

Mathieu, Martin

doi:10.1090/S0002-9939-03-07215-0

Spectrally bounded operators on simple $C^{*}$-algebras
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by Martin Mathieu

Proc. Amer. Math. Soc. 132 (2004), 443-446

DOI: https://doi.org/10.1090/S0002-9939-03-07215-0

Published electronically: August 7, 2003

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Abstract:

A linear mapping $T$ from a subspace $E$ of a Banach algebra into another Banach algebra is called spectrally bounded if there is a constant $M\geq 0$ such that $r(Tx)\leq M r(x)$ for all $x\in E$, where $r( \cdot )$ denotes the spectral radius. We prove that every spectrally bounded unital operator from a unital purely infinite simple $C^*$-algebra onto a unital semisimple Banach algebra is a Jordan epimorphism.

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