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Sublattices of the banach envelope of weak
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:
We prove that every separable Banach lattice is lattice isometric to a closed sublattice of the Banach envelope of Weak
References:
- 1.
- M. Cwikel and C. Fefferman, Maximal seminorms on Weak
, Studia Math. 69 (1980), 149-154. MR 83b:46033 - 2.
- M. Cwikel and C. Fefferman, The canonical seminorm on Weak
, Studia Math. 78 (1984), 275-278. MR 86i:46030 - 3.
- N. J. Kalton, Banach space embeddings into
, Israel J. Math 52 (1985), 305-319. MR 87k:46045 - 4.
- J. Kupka and N. T. Peck, The
structure of Weak , Math. Ann. 269 (1984), 235-262. - 5.
- H. P. Lotz, Extensions and liftings of positive linear mappings on Banach lattices, Trans. Amer. Math. Soc. 211 (1975), 85-100. MR 52:4022
- 6.
- H. P. Lotz,
convergence in the dual of Weak , Israel J. Math. (to appear). - 7.
- H. P. Lotz, On the dual of the space Weak
. - 8.
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and in Banach lattices, Israel J. Math. 31 (1978), 169-179. MR 80g:46023 - 9.
- N. T. Peck and M. Talagrand, Banach sublattices of weak
, 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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