J. da Providência; Natalia Bebiano; Ricardo Emanuel Cunha Teixeira;
Geometry of the numerical range of Krein space operators
The characteristic polynomial of the pencil generated by two J-Hermitian matrices is studied in connection with the numerical range. Geometric properties of the numerical range of linear operators on an indefinite inner product space are investigated. The point equation of the associated curve of the numerical range is derived, following Fiedler's approach for definite inner product spaces. The classification of the associated curve in the 3x3 case is presented, using Newton's classification of cubic curves. As a consequence, the respective numerical ranges are characterized. Illustrative examples of all the different possibilities are given.
Pré-publicações do Departamento de Matemática da Universidade de Coimbra