A small Banach space $C(K)$ without nice renormings

Todor Manev; Damian Sobota; Lyubomyr Zdomskyy

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arXiv · 2606.13294

A small Banach space $C(K)$ without nice renormings

Todor Manev·Damian Sobota·Lyubomyr Zdomskyy

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Abstract

We prove that consistently $\omega_1<\mathfrak{c}$ and there exists a compact space $K$ whose Banach space $C(K)$ of continuous real-valued functions is Grothendieck, has density $\omega_1$, and admits no renorming which is strictly convex or sequentially Kadets--Klee.

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Todor Manev, Damian Sobota, Lyubomyr Zdomskyy. 2026-06-11. A small Banach space $C(K)$ without nice renormings. https://arxiv.org/abs/2606.13294

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