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Journal of Convex Analysis 08 (2001), No. 2, 291--326
Copyright Heldermann Verlag 2001

Invariant Convex Sets in Operator Lie Algebras

Andreas Neumann
Fachbereich Mathematik, Technische Universitšt, Schlossgartenstr. 7, 64289 Darmstadt, Germany

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 }.

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