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Metric Markov cotype of ℓ $_{1}$ and Hilbert-space Lipschitz extension

Proves that real ℓ

_{1}

has metric Markov cotype two, answering Mendel and Naor's question. Consequently, every Lipschitz map from an arbitrary subset of a real Hilbert space into ℓ

_{1}

extends to the whole space with a universal multiplicative loss in its Lipschitz constant, resolving Ball's extension problem for this target.

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Metric Markov Cotype Two of ℓ $_{1}$

Oct 5, 2026·l1-markov-cotype.pdf

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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Metric Markov cotype of ℓ1_{1}1​ and Hilbert-space Lipschitz extension

Manuscripts in this family · 1

Metric Markov Cotype Two of ℓ1_{1}1​

Metric Markov cotype of ℓ $_{1}$ and Hilbert-space Lipschitz extension

Metric Markov Cotype Two of ℓ $_{1}$