It is shown that a Banach space admits an equivalent norm whose modulus of uniform convexity has power-type p if and only if it is Markov p-convex. Counterexamples are constructed to natural questions related to isomorphic uniform convexity of metric spaces, showing in particular that tree metrics fail to have the dichotomy property.
|Original language||English (US)|
|Number of pages||51|
|Journal||Journal of the European Mathematical Society|
|State||Published - 2013|
ASJC Scopus subject areas
- Applied Mathematics