Abstract

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:(∀j) fj(X)≤cj}C = \{X : (\forall j)\, f_j(X) \leq c_j\}

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Andreas Neumann

Fachbereich Mathematik, Technische Universität, Schlossgartenstr. 7, 64289 Darmstadt, Germany

References

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Suggested citation

A. Neumann. “Invariant Convex Sets in Operator Lie Algebras.” Journal of Convex Analysis 8 (2001), No. 2, 291–326. https://doi.org/10.68381/jca08015

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Published by Heldermann Verlag, 2001. Rights now held by Banach Press LLC.