The Elliptical and the Hyperbolical Range Theorems Revisited

Teixeira, Ricardo Emanuel Cunha; Bebiano, Natália; Providência, João da

http://hdl.handle.net/10400.3/1340

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Authors

Teixeira, Ricardo Emanuel Cunha

Bebiano, Natália

Providência, João da

Abstract(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.

Description

International Conference on Engineering and Mathematics (ENMA'2007), July 9-11, 2007 - Bilbao, Spain.

Keywords

Generalized Numerical Range Indefinite Inner Product Space Plane Algebraic Curve Numerical Range

URI

http://hdl.handle.net/10400.3/1340

Citation

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".