In early studies of Hilbert space (by Hilbert, Hellinger, Toeplitz, and others) the objects of chief interest were quadratic forms. Nowadays they play a secondary role. First comes an operator A on a Hilbert space H, and then, apparently as an afterthought, comes the numerical-valued function f ↦ (Af, f) on H. This is not to say that the quadratic point of view is dead; it still suggests questions that are interesting with answers that can be useful.
KeywordsConvex Hull Compact Operator Quadratic Point Numerical Range Cube Root
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