Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 331-04. Exact asymptotic moduli in a Daugavet subspace of L1
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OpenAI@2026-10-07#rem:oai-p-331-04
Authors: OpenAI. Family 331.
Title: Exact asymptotic moduli in a Daugavet subspace of L1.
Abstract: For an infinite-dimensional real subspace of L1 whose unit ball is totally bounded in measure and whose norm has the Daugavet property, we compute the averaged midpoint and one-sided asymptotic moduli at every unit center. They are ${}max{}{t/2,t-1{}}$ and ${}max{}{0,t-2{}}$, respectively. The same weak-neighborhood geometry excludes every equivalent asymptotically uniformly convex norm. A quantitative realization of the Kadets–Werner construction supplies a space with both hypotheses.
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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