Lorentz spaces that are isomorphic to subspaces of $L^ 1$
HTML articles powered by AMS MathViewer
- by Carsten Schütt
- Trans. Amer. Math. Soc. 314 (1989), 583-595
- DOI: https://doi.org/10.1090/S0002-9947-1989-0974527-8
- PDF | Request permission
Abstract:
We show which Lorentz spaces are isomorphic to subspaces of ${L^1}$ and which are not.References
- Jean Bretagnolle and Didier Dacunha-Castelle, Application de l’étude de certaines formes linéaires aléatoires au plongement d’espaces de Banach dans des espaces $L^{p}$, Ann. Sci. École Norm. Sup. (4) 2 (1969), 437–480 (French). MR 265930
- J. Creekmore, Type and cotype in Lorentz $L_{pq}$ spaces, Nederl. Akad. Wetensch. Indag. Math. 43 (1981), no. 2, 145–152. MR 707247 D. Dacunha-Castelle, Variables aléatoires échangeables et espaces d’Orlicz, Séminaire Maurey-Schwartz 1974-75, exposés 10 et 11, Ecole Polytéchnique, Paris.
- Ed Dubinsky, A. Pełczyński, and H. P. Rosenthal, On Banach spaces $X$ for which $\Pi _{2}({\cal L}_{\infty },\,X)=B({\cal L}_{\infty },\,X)$, Studia Math. 44 (1972), 617–648. MR 365097, DOI 10.4064/sm-44-6-617-648 G. H. Hardy, J. E. Littlewood and G. Polya, Inequalities, Cambridge Univ. Press, 1934.
- W. B. Johnson, B. Maurey, G. Schechtman, and L. Tzafriri, Symmetric structures in Banach spaces, Mem. Amer. Math. Soc. 19 (1979), no. 217, v+298. MR 527010, DOI 10.1090/memo/0217
- Stanisław Kwapień and Carsten Schütt, Some combinatorial and probabilistic inequalities and their application to Banach space theory, Studia Math. 82 (1985), no. 1, 91–106. MR 809774, DOI 10.4064/sm-82-1-91-106 —, Some combinatorial and probabilistic inequalities and their application to Banach space theory. II, preprint.
- J. Lindenstrauss and A. Pełczyński, Absolutely summing operators in $L_{p}$-spaces and their applications, Studia Math. 29 (1968), 275–326. MR 231188, DOI 10.4064/sm-29-3-275-326
- Joram Lindenstrauss and Lior Tzafriri, Classical Banach spaces. I, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 92, Springer-Verlag, Berlin-New York, 1977. Sequence spaces. MR 0500056
- Y. Raynaud and C. Schütt, Some results on symmetric subspaces of $L_1$, Studia Math. 89 (1988), no. 1, 27–35. MR 951082, DOI 10.4064/sm-89-1-27-35
- Haskell P. Rosenthal, On the subspaces of $L^{p}$ $(p>2)$ spanned by sequences of independent random variables, Israel J. Math. 8 (1970), 273–303. MR 271721, DOI 10.1007/BF02771562
- Shlomo Reisner, A factorization theorem in Banach lattices and its application to Lorentz spaces, Ann. Inst. Fourier (Grenoble) 31 (1981), no. 1, viii, 239–255 (English, with French summary). MR 613037
Bibliographic Information
- © Copyright 1989 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 314 (1989), 583-595
- MSC: Primary 46E30; Secondary 46B25
- DOI: https://doi.org/10.1090/S0002-9947-1989-0974527-8
- MathSciNet review: 974527