Metric Markov cotype of ℓ_(1) and Hilbert-space Lipschitz extension
OpenAI research collection · 1 manuscript · Source checked 2026-10-19
OpenAI's result summary
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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MANUSCRIPT 01
Metric Markov Cotype Two of ℓ_(1)
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…
Full source abstract
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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