Krein space, Joint numerical range, Convexity
This note investigates the convexity of the indefinite joint numerical range of a tuple of Hermitian matrices in the setting of Krein spaces. Its main result is a necessary and sufficient condition for convexity of this set. A new notion of “quasi-convexity” is introduced as a refinement of pseudo-convexity.
Nakazato, Hiroshi; Bebiano, Natalia; and da Providencia, Joao.
"A note on the convexity of the indefinite joint numerical range",
Electronic Journal of Linear Algebra,