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• # Artykuł - szczegóły

## Studia Mathematica

2009 | 192 | 2 | 97-110

## Canonical Banach function spaces generated by Urysohn universal spaces. Measures as Lipschitz maps

EN

### Abstrakty

EN
It is proved (independently of the result of Holmes [Fund. Math. 140 (1992)]) that the dual space of the uniform closure $CFL(𝕌_{r})$ of the linear span of the maps x ↦ d(x,a) - d(x,b), where d is the metric of the Urysohn space $𝕌_{r}$ of diameter r, is (isometrically if r = +∞) isomorphic to the space $LIP(𝕌_{r})$ of equivalence classes of all real-valued Lipschitz maps on $𝕌_{r}$. The space of all signed (real-valued) Borel measures on $𝕌_{r}$ is isometrically embedded in the dual space of $CFL(𝕌_{r})$ and it is shown that the image of the embedding is a proper weak* dense subspace of $CFL(𝕌_{r})*$. Some special properties of the space $CFL(𝕌_{r})$ are established.

97-110

wydano
2009

### Twórcy

autor
• Institute of Mathematics, Jagiellonian University, Łojasiewicza 6, 30-348 Kraków, Poland