Isometric embeddings into $C(K)$-spaces doing stable phase retrieval

Abstract

Motivated by a question posed by Freeman, Oikhberg, Pineau and Taylor, we prove that if $K$ is a compact Hausdorff space with $K^{(\hat{I}\pm )}\ne \varnothing$, where $2<\hat{I}\pm <\ddot{I}‰$, then $C[1,\ddot{I}{‰}^{\hat{I}}\pm ]$ isometrically embeds into $C(K)$ doing stable phase retrieval (SPR). We also show that the latter cannot be extended to the case $\hat{I}\pm =2$.

In this new edition, we have incorporated ideas from an independent paper by Jakub Rondoš and Damian Sobota to make a clearer presentation of our results. We thank them for bringing their paper to our attention