The Elliptical and the Hyperbolical Range Theorems Revisited
Ricardo Emanuel Cunha Teixeira, Natália Bebiano, João da Providência · Portuguese National Funding Agency for Science, Research and Technology (RCAAP Project by FCT) · 2007
A geometrical proof of the Hyperbolical Range Theorem, concerning the numerical range of linear operators on 2-dimensional Krein spaces, is given. The classical Elliptical Range Theorem, which is the correspondent result for Hilbert spaces, is also obtained using the same technique. Both proofs depend on the geometrical properties of the plane algebraic curve that generates the numerical range as its convex hull or as its pseudoconvex hull.