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Spectrally bounded traces on C*-algebras

Published online by Cambridge University Press:  17 April 2009

Martin Mathieu
Martin Mathieu
Affiliation:
Department of Pure Mathematics, Queen's University Belfast, Belfast BT7 1NN, Northern Ireland e-mail: [email protected]
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Abstract

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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 ≥ 0 such that r(T x) ≤ Mr(x) for all x ∈ E, where r (·) denotes the spectral radius. We establish the equivalence of the following properties of a unital linear mapping T from a unital C* -algebra A into its centre:

(a) T is spectrally bounded;

(b) T is a spectrally bounded trace;

(c) T is a bounded trace.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 68 , Issue 1 , August 2003 , pp. 169 - 173
Copyright
Copyright © Australian Mathematical Society 2003

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