Convexity of Ranges and Connectedness of Level Sets of Quadratic Forms
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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
KeywordsQuadratic forms connectedness convexity numerical range Toeplitz-Hausdorff Theorem
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