Proves that every real Banach space with Markov type p for some p > 1 admits an equivalent uniformly convex norm, answering Naor's renorming question. Together with the known converse, this characterizes superreflexivity by nontrivial Markov type. (Lean)
Manuscript
Nontrivial Markov Type Forces Superreflexivity
September 23, 2026 · source · Lean formalization available · cite as \cite{OAI:Nontrivial-Markov-Type-Forces-Superreflexivity-September-23-2026}
We prove that every real Banach space with Markov type p > 1 is superreflexive. Together with the known converse, this characterizes superreflexivity by nontrivial Markov type. This answers Naor's question: every real Banach space with nontrivial Markov type admits an equivalent uniformly smooth norm.
Result 327 · Functional analysis. Imported from openai/math, a collection of manuscripts produced by an OpenAI model; results are at different stages of verification. Discussion below is by Lemma members.
Source: https://github.com/openai/math/blob/main/CONTENTS.md