A representation theorem for $L^{p}$ spaces
HTML articles powered by AMS MathViewer
- by Marek Kanter
- Proc. Amer. Math. Soc. 31 (1972), 472-474
- DOI: https://doi.org/10.1090/S0002-9939-1972-0290088-6
- PDF | Request permission
Abstract:
Using the theory of symmetric stable process of index $p \in (0,2]$, we prove that if a sepaéable Frechet space $L$ has all its finite dimensional subspaces linearly isometric with a subspace of ${L^p}[0,1]$ then $L$ itself is linearly isometric with a subspace of ${L^p}[0,1]$.References
- Jean Bretagnolle, Didier Dacunha-Castelle, and Jean-Louis Krivine, Lois stables et espaces $L^{p}$, Ann. Inst. H. Poincaré Sect. B (N.S.) 2 (1965/1966), 231–259 (French). MR 0203757
- Nelson Dunford and Jacob T. Schwartz, Linear Operators. I. General Theory, Pure and Applied Mathematics, Vol. 7, Interscience Publishers, Inc., New York; Interscience Publishers Ltd., London, 1958. With the assistance of W. G. Bade and R. G. Bartle. MR 0117523 P. Levy, Théorie de l’addition des variables aléatoires, Gauthier-Villars, Paris, 1925.
- Michael Schilder, Some structure theorems for the symmetric stable laws, Ann. Math. Statist. 41 (1970), 412–421. MR 254915, DOI 10.1214/aoms/1177697080
Bibliographic Information
- © Copyright 1972 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 31 (1972), 472-474
- MSC: Primary 46.35
- DOI: https://doi.org/10.1090/S0002-9939-1972-0290088-6
- MathSciNet review: 0290088