Abstract

We show that the Carathéodory number of the joint numerical range of d many bounded self-adjoint operators is at most d-1, and even at most d-2 if the underlying Hilbert space has dimension at least 3. This extension of the classical convexity results for numerical ranges shows that also joint numerical ranges are significantly less non-convex than general sets.

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Keywords

  • Joint numerical range
  • convexity
  • Caratheodory number

Mathematics Subject Classification

47A12, 52A05

References

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Suggested citation

B. Maier, T. Netzer. “A Note on the Carathéodory Number of the Joint Numerical Range.” Journal of Convex Analysis 33 (2026), No. 1&2, 517–519. https://doi.org/10.68381/jca33032

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Published by Heldermann Verlag, 2026. Rights now held by Banach Press.