Isometric embeddings into $C(K)$-spaces doing stable phase retrieval
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915822801256448 |
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| author | García-Sánchez, Enrique de Hevia, David |
| author_facet | García-Sánchez, Enrique de Hevia, David |
| contents | Motivated by a question posed by Freeman, Oikhberg, Pineau and Taylor, we prove that if $K$ is a compact Hausdorff space with $K^{(α)}\neq\varnothing$, where $2<α<ω$, then $C[1,ω^α]$ isometrically embeds into $C(K)$ doing stable phase retrieval (SPR). We also show that the latter cannot be extended to the case $α=2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_08110 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Isometric embeddings into $C(K)$-spaces doing stable phase retrieval García-Sánchez, Enrique de Hevia, David Functional Analysis 46B04, 46B42, 46E15 Motivated by a question posed by Freeman, Oikhberg, Pineau and Taylor, we prove that if $K$ is a compact Hausdorff space with $K^{(α)}\neq\varnothing$, where $2<α<ω$, then $C[1,ω^α]$ isometrically embeds into $C(K)$ doing stable phase retrieval (SPR). We also show that the latter cannot be extended to the case $α=2$. |
| title | Isometric embeddings into $C(K)$-spaces doing stable phase retrieval |
| topic | Functional Analysis 46B04, 46B42, 46E15 |
| url | https://arxiv.org/abs/2512.08110 |