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

• Autorzy: Piotr Niemiec
• Języki publikacji: 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.

Kategorie tematyczne

• 26A16: Lipschitz (H\"older) classes
• 46E27: Spaces of measures

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2009
• Tom: 192
• Numer: 2
• Strony: 97-110

Daty

wydano

2009

Twórcy

autor

Piotr Niemiec

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

Identyfikatory

DOI

10.4064/sm192-2-1