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The Quarterly Journal of Mathematics Advance Access originally published online on February 9, 2007
The Quarterly Journal of Mathematics 2007 58(2):249-253; doi:10.1093/qmath/hal024
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© 2007. Published by Oxford University Press. All rights reserved. For permissions, please email: journals.permissions@oxfordjournals.org

JORDAN ISOMORPHISM OF PURELY INFINITE C*-ALGEBRAS

Ying-Fen Lin1,2,{dagger} and Martin Mathieu3

1 Department of Mathematics, National Hualien University of Education, Hualien 970-03, Taiwan
2 Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta T6G 2G1, Canada
3 Department of Pure Mathematics, Queen's University Belfast, Belfast BT7 1NN, Northern Ireland

{dagger} Corresponding author. E-mail: linyf{at}mail.nhlue.edu.tw

Received 17 May 2006;
  Abstract

We prove that every unital bounded linear mapping from a unital purely infinite C*-algebra of real rank zero into a unital Banach algebra which preserves elements of square zero is a Jordan homomorphism. This entails a description of unital surjective spectral isometries as the Jordan isomorphisms in this setting.


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