Spectrally bounded operators on simple C^{}-algebras

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 Mr(x) for all x\in E, where r(·) denotes the spectral radius. We prove that every spectrally bounded unital operator from a unital pure...

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Bibliographic Details
Published in:Proceedings of the American Mathematical Society 2004-02, Vol.132 (2), p.443-446
Main Author: Mathieu, Martin
Format: Article
Language:English
Subjects:
Algebra
Commutators
Exact sciences and technology
Finite sums
Functional analysis
Homomorphisms
Linear transformations
Mathematical analysis
Mathematical theorems
Mathematics
Nonassociative rings and algebras
Operator theory
Sciences and techniques of general use
Von Neumann algebra
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Summary: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 Mr(x) for all x\in E, where r(·) 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.
ISSN:0002-9939
1088-6826
DOI:10.1090/S0002-9939-03-07215-0