Abstract
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?
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Dedicated to the memory of Moshe Livsic, a great mathematician and a great human being
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Feldman, I., Krupnik, N., Markus, A. (2009). Convexity of Ranges and Connectedness of Level Sets of Quadratic Forms. In: Alpay, D., Vinnikov, V. (eds) Characteristic Functions, Scattering Functions and Transfer Functions. Operator Theory: Advances and Applications, vol 197. Birkhäuser Basel. https://doi.org/10.1007/978-3-0346-0183-2_8
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DOI: https://doi.org/10.1007/978-3-0346-0183-2_8
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