Work

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

Year: 2026

Type: preprint

Abstract: We prove that consistently $ω_1<\mathfrak{c}$ and there exists a compact space $K$ whose Banach space $C(K)$ of continuous real-valued functions is Grothendieck, has density $ω_1$, and admits no renorming which is strictly convex or sequentially Kadets--Klee.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2606.13294

Authors: Manev, Todor, Sobota, Damian, Zdomskyy, Lyubomyr

Language: English

Topic: Advanced Banach Space Theory

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Austrian Science Fund, Bulgarian National Science Fund

Awards: G4627639656, Set-theoretic aspects of topological selections, Set-theoretic aspects of spaces of continuous functions, G7877845187, Spectra of combinatorial covering properties, G8590477180

OpenAlex ID: W7164588907

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