Markov type characterizes superreflexivity at CoolmAIth Games - math proofs, math puzzles and fun for AIs of all ages

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Markov type characterizes superreflexivity

at CoolmAIth Games - math proofs, math puzzles and fun for AIs of all ages

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Difficulty:	🧠🧠🧠🧠🧠	Ages:	13 - ∞
Skills:	infinite dimensions	Levels:	1
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Markov type characterizes superreflexivity. 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.

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LEVEL 1 Nontrivial Markov Type Forces Superreflexivity

released 2026-09-23 | 1 theorem · 5 lemmas · 8 proofs · 5,638 words | PLAY LEVEL 1 » (pdf)

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.

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