Geodesic
Non-linear Jordan triple automorphisms of sets of self-adjoint matrices and operators
Lajos Molnár1
1 Institute of Mathematics University of Debrecen P.O. Box 12 H-4010 Debrecen, Hungary
Studia Mathematica, Tome 173 (2006) no. 1, pp. 39-48

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

We consider the so-called Jordan triple automorphisms of some important sets of self-adjoint operators without the assumption of linearity. These transformations are bijective maps which satisfy the equality $$ \phi(ABA)=\phi(A)\phi(B)\phi(A) $$ on their domains. We determine the general forms of these maps (under the assumption of continuity) on the sets of all invertible positive operators, of all positive operators, and of all invertible self-adjoint operators.
DOI : 10.4064/sm173-1-3
Keywords: consider so called jordan triple automorphisms important sets self adjoint operators without assumption linearity these transformations bijective maps which satisfy equality phi aba phi phi phi their domains determine general forms these maps under assumption continuity sets invertible positive operators positive operators invertible self adjoint operators

Lajos Molnár 1

1 Institute of Mathematics University of Debrecen P.O. Box 12 H-4010 Debrecen, Hungary 
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Lajos Molnár. Non-linear Jordan triple automorphisms of sets of
self-adjoint matrices and operators. Studia Mathematica, Tome 173 (2006) no. 1, pp. 39-48. doi: 10.4064/sm173-1-3

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