A superreflexive space is a Banach space for which every Banach space finitely representable in it is reflexive. Finite representability means that each finite-dimensional subspace can be linearly embedded into the original space with distortion arbitrarily close to 1. Equivalently, a superreflexive space admits an equivalent uniformly convex norm. This is an existence statement about a renorming, not a requirement that the specified norm already be uniformly convex.
Superreflexive Space
See also
Banach Space, Markov Type, Reflexive Space, Uniformly ConvexExplore with Wolfram|Alpha
References
Dilworth, S. J.; Kutzarova, D.; Randrianarivony, N. L.; and Romney, M. "Sums of Asymptotically Midpoint Uniformly Convex Spaces." Bull. Belg. Math. Soc. Simon Stevin 24, 439-446, 2017. https://doi.org/10.36045/bbms/1506477692.James, R. C. "Super-Reflexive Banach Spaces." Canad. J. Math. 24, 896-904, 1972. https://doi.org/10.4153/CJM-1972-089-7.Cite this as:
Weisstein, Eric W. "Superreflexive Space." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/SuperreflexiveSpace.html