Copyright © 2011 Abdolaziz Abdollahi and Mohammad Taghi Heydari. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We consider the spatial numerical range of operators on weighted Hardy spaces and give conditions for closedness of numerical range of compact operators. We also prove that the spatial numerical range of finite rank operators on weighted Hardy spaces is star shaped; though, in general, it does not need to be convex.