Abstract
Motivated by noncommutative geometry and quantum physics, the concept of metric operator field is introduced. Roughly speaking, a metric operator field is a vector field on a set with values in self-tensor product of a bundle of C*-algebras, satisfying properties similar to an ordinary metric. It is proved that to any such object there naturally correspond a Banach *-algebra that we call Lipschitz algebra, a class of probabilistic metrics, and a continuous field of C*-algebras in the sense of Dixmier. It is proved that for metric operator fields with values in von Neumann algebras the associated Lipschitz algebras are dual Banach spaces, and under some conditions, they are not amenable Banach algebras. Some examples and constructions are considered. We also discuss very briefly a possible application to quantum gravity.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
More From: Iranian Journal of Science and Technology, Transactions A: Science
Disclaimer: 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.