Abstract
If E E belongs to a certain category of Banach spaces (the B ∞ {B^\infty } -smooth spaces) which include Hilbert spaces and if F F is any normed space, it is proved that any local linear automorphism of C ∞ ( E , F ) {C^\infty }(E,F) is a differential operator. This generalizes a result of J. Peetre when E = R n E = {R^n} and F = R F = R .
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.
