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

Enrique García-Sánchez; David de Hevia

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

Functional Analysis 2026-03-02 v2

Authors: Enrique García-Sánchez , David de Hevia

Abstract

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

Keywords

metric embeddings

Cite

@article{arxiv.2512.08110,
  title  = {Isometric embeddings into $C(K)$-spaces doing stable phase retrieval},
  author = {Enrique García-Sánchez and David de Hevia},
  journal= {arXiv preprint arXiv:2512.08110},
  year   = {2026}
}

Comments

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

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

Abstract

Keywords

Cite

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