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The Elliptical and the Hyperbolical Range Theorems Revisited
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Orientador(es)
Resumo(s)
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.
Descrição
International Conference on Engineering and Mathematics (ENMA'2007), July 9-11, 2007 - Bilbao, Spain.
Palavras-chave
Generalized Numerical Range Indefinite Inner Product Space Plane Algebraic Curve Numerical Range
Contexto Educativo
Citação
Teixeira, Ricardo; Bebiano, Natália; Providência, João da. The Elliptical and the Hyperbolical Range Theorems Revisited. In "Proceedings of the International Conference on Engineering and Mathematics (ENMA 2007), Bilbao, 2007".