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Order and Spectrum Preserving Maps on Positive Operators

  Published:2016-12-06
 Printed: Dec 2017
  • Peter Ċ emrl,
    Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, SI-1000 Ljubljana, Slovenia
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Abstract

We describe the general form of surjective maps on the cone of all positive operators which 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: spectrum preserver, order preserver, positive operator spectrum preserver, order preserver, positive operator
MSC Classifications: 47B49 show english descriptions Transformers, preservers (operators on spaces of operators) 47B49 - Transformers, preservers (operators on spaces of operators)
 

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