An ${\mathrm{\ell }}^1$-Isometric Subspace of $C[0,1]$ with Countable Oscillating Spectrum

In this paper we construct a closed subspace $X\subset C[0,1]$ with countable oscillating spectrum $\mathrm{\Omega }(X)$ such that $X$ is isometric to ${\mathrm{\ell }}^1$. This provides a negative answer to Question~4.3 posed by Enflo, Gurariy, and Seoane in [Trans. Amer. Math. Soc. $\mathbf{\text{366}}$ (2014)].