Abstract

For every superreflexive Banach space X there exists a supermultiplicative function which is the supremum, in a very natural ordering, of the set of all the moduli of convexity of equivalent norms. If this supremum is actually a maximum achieved under some equivalent renorming of X, then its modulus of convexity is the best possible in asymptotic sense. Otherwise, we can give an almost optimal uniformly convex renorming of X beyond the classical power type bound obtained by Pisier [21].

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 call

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.