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Transactions of the American Mathematical Society

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Lorentz spaces that are isomorphic to subspaces of $ L\sp 1$


Author: Carsten Schütt
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
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Abstract: We show which Lorentz spaces are isomorphic to subspaces of $ {L^1}$ and which are not.


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  • [1] J. Bretagnolle and D. Dacunha-Castelle, Application de l'étude de certaines formes linéaires aléatoires au plongement d'espaces de Banach dans les espaces $ {L^p}$, Ann. Sci. Ecole Norm. Sup. (4) 2 (1969), 437-480. MR 0265930 (42:839)
  • [2] J. Creekmore, Type and cotype in Lorentz $ {L_{p,q}}$ spaces, Indag. Math. 43 (1981), 145-152. MR 707247 (84i:46032)
  • [3] D. Dacunha-Castelle, Variables aléatoires échangeables et espaces d'Orlicz, Séminaire Maurey-Schwartz 1974-75, exposés 10 et 11, Ecole Polytéchnique, Paris.
  • [4] E. Dubinski, A. Pelczyński and H. P. Rosenthal, On Banach spaces $ X$ for which $ {\pi _2}({\mathcal{L}_\infty },X) = B({\mathcal{L}_\infty },X)$, Studia Math. 44 (1972), 617-634. MR 0365097 (51:1350)
  • [5] G. H. Hardy, J. E. Littlewood and G. Polya, Inequalities, Cambridge Univ. Press, 1934.
  • [6] W. B. Johnson, B. Maurey, G. Schechtman and L. Tzafriri, Symmetric structures in Banach spaces, Mem. Amer. Math. Soc. No. 217, 1979. MR 527010 (82j:46025)
  • [7] S. Kwapień and C. Schütt, Some combinatorial and probabilistic inequalities and their application to Banach space theory, Studia Math. 82 (1985), 91-106. MR 809774 (87h:46042)
  • [8] -, Some combinatorial and probabilistic inequalities and their application to Banach space theory. II, preprint.
  • [9] J. Lindenstrauss and A. Pelczyński, Absolutely summing operators in $ {L_p}$-spaces and their applications, Studia Math. 29 (1968), 275-326. MR 0231188 (37:6743)
  • [10] J. Lindenstrauss and L. Tzafriri, Classical Banach spaces. I, II, Springer-Verlag, 1977 and 1979. MR 0500056 (58:17766)
  • [11] Y. Raynaud and C. Schütt, Some results on symmetric subspaces of $ {L^1}$, Studia Math. 89 (1988), 27-35. MR 951082 (89g:46057)
  • [12] H. 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 0271721 (42:6602)
  • [13] S. Reisner, A factorization theorem in Banach lattices and its application to Lorentz spaces, Ann. Inst. Fourier (Grenoble) 31 (1981), 239-255. MR 613037 (82g:46066)

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DOI: https://doi.org/10.1090/S0002-9947-1989-0974527-8
Article copyright: © Copyright 1989 American Mathematical Society

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