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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(e) ISSN 0002-9939(p)

     

Sublattices of the banach envelope of weak $L^{1}$

Author(s): Heinrich P. Lotz; N. T. Peck
Journal: Proc. Amer. Math. Soc. 126 (1998), 75-84.
MSC (1991): Primary 46B30, 46E30
MathSciNet review: 1343710
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Abstract | References | Similar articles | Additional information

Abstract: We prove that every separable Banach lattice is lattice isometric to a closed sublattice of the Banach envelope of Weak $L^{1}.$


References:

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N. J. Kalton, Banach space embeddings into $L_{0}$, Israel J. Math 52 (1985), 305-319. MR 87k:46045

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J. Kupka and N. T. Peck, The $L_{1}$ structure of Weak $L^{1}$, Math. Ann. 269 (1984), 235-262.

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H. P. Lotz, Extensions and liftings of positive linear mappings on Banach lattices, Trans. Amer. Math. Soc. 211 (1975), 85-100. MR 52:4022

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H. P. Lotz, $\text{Weak}^{\ast }$ convergence in the dual of Weak $L^{p}$, Israel J. Math. (to appear).

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H. P. Lotz, On the dual of the space Weak $L^{1}$.

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H. P. Lotz and H. P. Rosenthal, Embeddings of $C(\Delta )$ and $L^{1}[0,1]$ in Banach lattices, Israel J. Math. 31 (1978), 169-179. MR 80g:46023

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N. T. Peck and M. Talagrand, Banach sublattices of weak $L_1$, Israel J. Math 59 (1987), 257-271. MR 89a:46045


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Additional Information:

Heinrich P. Lotz
Affiliation: Department of Mathematics, University of Illinois, Urbana, Illinois 61801

N. T. Peck
Affiliation: Department of Mathematics, University of Illinois, Urbana, Illinois 61801

DOI: 10.1090/S0002-9939-98-03506-0
PII: S 0002-9939(98)03506-0
Keywords: Banach lattice, Banach envelope, Lorentz space, Weak $L^{1}, $ Weak $L^{p}, $ lattice isometry, order isometry
Received by editor(s): March 13, 1995
Communicated by: Dale E. Alspach
Copyright of article: Copyright 1998, American Mathematical Society




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