Abstract
We study the Davis-Wielandt shell and the Davis-Wielandt radius of an operator on a normed linear space \(\mathcal {X}\). We show that after a suitable modification, the modified Davis-Wielandt radius defines a norm on \(\mathcal {L}(\mathcal {X})\) which is equivalent to the usual operator norm on \(\mathcal {L}(\mathcal {X})\). We introduce the Davis-Wielandt index of a normed linear space and compute its value explicitly in case of some particular polyhedral Banach spaces. We also present a general method to estimate the Davis-Wielandt index of any polyhedral finite-dimensional Banach space.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
