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.



To view the content in your browser, please download Adobe Reader or, alternately,
you may Download the file to your hard drive.

NOTE: The latest versions of Adobe Reader do not support viewing PDF files within Firefox on Mac OS and if you are using a modern (Intel) Mac, there is no official plugin for viewing PDF files within the browser window.