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Order and Spectrum Preserving Maps on Positive Operators

Published online by Cambridge University Press:  20 November 2018

Peter Šemrl
Peter Šemrl*
Affiliation:
Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, SI-10000 Ljubljana, Slovenia e-mail: peter.semrl@fmf.uni-lj.si
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Abstract

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We describe the general form of surjective maps on the cone of all positive operators that preserve order and spectrum. The result is optimal as shown by counterexamples. As an easy consequence, we characterize surjective order and spectrum preserving maps on the set of all self-adjoint operators.

Keywords

47B49spectrum preserverorder preserverpositive operator
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 69 , Issue 6 , 01 December 2017 , pp. 1422 - 1435
Copyright
Copyright © Canadian Mathematical Society 2016

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