On regular operators extending (pseudo)metrics
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911286330130432 |
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| author | Banakh, Taras |
| author_facet | Banakh, Taras |
| contents | It is proved that for every stratifiable space $Y$ and a closed subset $X\subset Y$ there exists a regular (i.e. linear positive with unit norm) extension operator $T:C(X\times X)\to C(Y\times Y)$ preserving the class of (pseudo)metrics. This operator is continuous with respect to the pointwise as well as to the compact-open topologies on the linear lattices of continuous functions $C(X\t X)$ and $C(Y\t Y)$. If moreover the space Y is metrizable then the operator $T$ preserves the class of admissible metrics. The equivariant analog of the above statement is proved as well. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_20374 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On regular operators extending (pseudo)metrics Banakh, Taras Functional Analysis General Topology 54C20, 54C35, 54E20, 54E35 It is proved that for every stratifiable space $Y$ and a closed subset $X\subset Y$ there exists a regular (i.e. linear positive with unit norm) extension operator $T:C(X\times X)\to C(Y\times Y)$ preserving the class of (pseudo)metrics. This operator is continuous with respect to the pointwise as well as to the compact-open topologies on the linear lattices of continuous functions $C(X\t X)$ and $C(Y\t Y)$. If moreover the space Y is metrizable then the operator $T$ preserves the class of admissible metrics. The equivariant analog of the above statement is proved as well. |
| title | On regular operators extending (pseudo)metrics |
| topic | Functional Analysis General Topology 54C20, 54C35, 54E20, 54E35 |
| url | https://arxiv.org/abs/2511.20374 |