Geodesic
Order and Spectrum Preserving Maps on Positive Operators
Canadian journal of mathematics, Tome 69 (2017) no. 6, pp. 1422-1435

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DOI

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.
DOI : 10.4153/CJM-2016-039-0
Mots-clés : 47B49, spectrum preserver, order preserver, positive operator 
Šemrl, Peter. Order and Spectrum Preserving Maps on Positive Operators. Canadian journal of mathematics, Tome 69 (2017) no. 6, pp. 1422-1435. doi: 10.4153/CJM-2016-039-0
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     author = {\v{S}emrl, Peter},
     title = {Order and {Spectrum} {Preserving} {Maps} on {Positive} {Operators}},
     journal = {Canadian journal of mathematics},
     pages = {1422--1435},
     year = {2017},
     volume = {69},
     number = {6},
     doi = {10.4153/CJM-2016-039-0},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-2016-039-0/}
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