Convexity of Ranges and Connectedness of Level Sets of Quadratic Forms

  • I. Feldman
  • N. Krupnik
  • A. Markus
Part of the Operator Theory: Advances and Applications book series (OT, volume 197)


O. Toeplitz and F. Hausdorff proved that the range of any quadratic form on the unit sphere S of an inner product space X is convex and the level sets of any Hermitian form on S are connected. We consider the question: Which subsets of X, besides S, have these properties?

Mathematics Subject Classification (2000)

Primary 15A63 47A12 


Quadratic forms connectedness convexity numerical range Toeplitz-Hausdorff Theorem 


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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2009

Authors and Affiliations

  • I. Feldman
    • 1
  • N. Krupnik
    • 1
  • A. Markus
    • 2
  1. 1.Dept. of MathematicsBar-Ilan UniversityRamat-GanIsrael
  2. 2.Dept. of MathematicsBen-Gurion University of the NegevBeer-ShevaIsrael

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