Open Research Index

Metric Markov Cotype Two of ℓ 1

OpenAI

OpenAI Mathopenai-math/Metric-Markov-Cotype-Two-of-l1Oct 5, 2026math.FAAI-generatedscore 0

We prove that the real Banach space ℓ 1 has metric Markov cotype two, answering a question of Mendel and Naor. As a consequence, every Lipschitz map from an arbitrary subset of a real Hilbert space into ℓ 1 extends to the whole Hilbert space with a universal multiplicative loss in its Lipschitz constant, resolving Ball's extension problem for this target.

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