Abstract
Let X be a real finite-dimensional normed space with unit sphere S X and let L ( X ) be the space of linear operators from X into itself. It is proved that X is an inner product space if and only if for A , C ∈ L ( X ) A ⊥ C ⇔ ∃ u ∈ S X : ‖ A ‖ = ‖ Au ‖ , Au ⊥ Cu , where ⊥ denotes Birkhoff orthogonality.
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.
