Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 330-01. A uniformly discrete counterexample to bounded approximation in Lipschitz-free spaces
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OpenAI@2026-10-07#rem:oai-p-330-01
Authors: OpenAI. Family 330.
Title: A uniformly discrete counterexample to bounded approximation in Lipschitz-free spaces.
Abstract: We construct a countable uniformly discrete metric space whose real Lipschitz-free space has the approximation property but fails the bounded approximation property, answering Kalton's question negatively. The identity can be approximated on every compact set by finite-rank operators, but no uniform bound on their norms is possible.
This abstract is a catalogue record. It is not a verification and not a premise. It does not close O.1. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted.
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