An $\ell^1$-Isometric Subspace of $C[0,1]$ with Countable Oscillating Spectrum
Functional Analysis
2025-10-06 v2
Abstract
In this paper we construct a closed subspace with countable oscillating spectrum such that is isometric to . This provides a negative answer to Question~4.3 posed by Enflo, Gurariy, and Seoane in [Trans. Amer. Math. Soc. \textbf{366} (2014)].
Cite
@article{arxiv.2509.26066,
title = {An $\ell^1$-Isometric Subspace of $C[0,1]$ with Countable Oscillating Spectrum},
author = {Geivison Ribeiro},
journal= {arXiv preprint arXiv:2509.26066},
year = {2025}
}
Comments
13 pages, keywords: Oscillating spectrum; Subspaces of continuous functions; Isometric embeddings; Banach space geometry, Lineability