Shapes and computer generation of numerical ranges of Krein space operators
Chi-Kwong Li, Leiba Rodman · Electronic Journal of Linear Algebra · 1998
Let (K; h; i) be a Hilbert space equipped with an inde nite inner product [ ;]. Then (K; [ ;]) is a (complex) Krein space. One can de ne the Krein space numerical range of an operator A acting on K as the collection of complex numbers of the form [Av; v] with v 2Ksatisfying [v; v] =1. In this paper, the shapes of Krein space numerical ranges of operators in the complex plane using the joint numerical range of self-adjoint operators on (K; h; i) are studied. Krein space numerical ranges of operators acting on a two-dimensional space are fully described. A Matlab program is developed to generate the sets in the nite dimensional case.