Abstract
AbstractLet X be a right C*‐module over a unital C*‐algebra . We study the Hopf fibration of X: where the projective space of X is the set of singly generated orthocomplemented submodules of X, is the set of elements of X, which generate such submodules, and module generated by . The group of unitary operators of the module X acts on both spaces. We introduce a Finsler metric in , which is invariant under the unitary action. Our main results establish that the map is distance decreasing (when the projective space of X is considered with its natural unitary invariant metric), and a minimality result in , characterizing metric geodesics in this space.
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.
