Abstract
ABSTRACTLet be a σ-finite measure space. Given a Banach space X, let the symbol stand for the unit sphere of X. We prove that the space of all complex-valued measurable essentially bounded functions equipped with the essential supremum norm satisfies the Mazur–Ulam property, that is, if X is any complex Banach space, every surjective isometry admits an extension to a surjective real linear isometry . This conclusion is derived from a more general statement which assures that every surjective isometry where K is a Stonean space, admits an extension to a surjective real linear isometry from onto X.
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.
