Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.00583 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912934287900672 |
|---|---|
| author | Enami, Yuta Matsuzaki, Izuho |
| author_facet | Enami, Yuta Matsuzaki, Izuho |
| contents | For a locally compact Hausdorff space $L$, we denote by $C_0(L,\mathbb{R})$ the Banach space of all continuous real-valued functions on $L$ vanishing at infinity, endowed with the supremum norm. In this paper, we prove that every surjective phase-isometry $T\colon S(C_0(X,\mathbb{R}))\to S(C_0(Y,\mathbb{R}))$ between the unit spheres of $C_0(X,\mathbb{R})$ and $C_0(Y,\mathbb{R})$ is a variant of a weighted composition operator in the following sense: there exist a function $\varepsilon\colon S(C_0(X,\mathbb{R}))\to\{-1,1\}$,a continuous function $α\colon Y\to \{-1,1\}$ and a homeomorphism $σ\colon Y\to X$ such that $T(f)(q)=\varepsilon(f)α(q)f(σ(q))$ for every $f\in S(C_0(X,\mathbb{R}))$ and $q\in Y$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_00583 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On phase-isometries between the unit spheres of the Banach space of continuous real-valued functions Enami, Yuta Matsuzaki, Izuho Functional Analysis For a locally compact Hausdorff space $L$, we denote by $C_0(L,\mathbb{R})$ the Banach space of all continuous real-valued functions on $L$ vanishing at infinity, endowed with the supremum norm. In this paper, we prove that every surjective phase-isometry $T\colon S(C_0(X,\mathbb{R}))\to S(C_0(Y,\mathbb{R}))$ between the unit spheres of $C_0(X,\mathbb{R})$ and $C_0(Y,\mathbb{R})$ is a variant of a weighted composition operator in the following sense: there exist a function $\varepsilon\colon S(C_0(X,\mathbb{R}))\to\{-1,1\}$,a continuous function $α\colon Y\to \{-1,1\}$ and a homeomorphism $σ\colon Y\to X$ such that $T(f)(q)=\varepsilon(f)α(q)f(σ(q))$ for every $f\in S(C_0(X,\mathbb{R}))$ and $q\in Y$. |
| title | On phase-isometries between the unit spheres of the Banach space of continuous real-valued functions |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2603.00583 |