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arXiv · 2607.12935

A Separable Banach Space with a Schauder Basis Which Is Not a Lipschitz Retract of Its Bidual

Antonio Acuaviva
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Abstract

We construct a separable Banach space $X$ with a Schauder basis such that $B_X$ is not a uniformly continuous retract of $B_{X^{**}}$. Consequently, $X$ is not a uniformly continuous retract of $X^{**}$ and hence is not a Lipschitz retract of $X^{**}$.

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Antonio Acuaviva. 2026-07-14. A Separable Banach Space with a Schauder Basis Which Is Not a Lipschitz Retract of Its Bidual. https://arxiv.org/abs/2607.12935

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