Geodesic
Invariant Convex Sets in Operator Lie Algebras
Journal of convex analysis, Tome 8 (2001) no. 2, pp. 291-326 
A. Neumann. Invariant Convex Sets in Operator Lie Algebras. Journal of convex analysis, Tome 8 (2001) no. 2, pp. 291-326. http://geodesic.mathdoc.fr/item/JCA_2001_8_2_JCA_2001_8_2_a0/
@article{JCA_2001_8_2_JCA_2001_8_2_a0,
     author = {A. Neumann},
     title = {Invariant {Convex} {Sets} in {Operator} {Lie} {Algebras}},
     journal = {Journal of convex analysis},
     pages = {291--326},
     year = {2001},
     volume = {8},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/JCA_2001_8_2_JCA_2001_8_2_a0/}
}
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Voir la notice de l'article provenant de la source Heldermann Verlag

We study the closed convex subsets of Lie algebras of bounded linear operators on a Hilbert space that are invariant under the corresponding group of unitary operators. We will give a family fj of convex functions such, that for each closed convex invariant set C there are real numbers cj satisfying C = { X : fj(X) ≤ cj for all j }.