Sublattices of the Banach envelope of weak $L^1$
HTML articles powered by AMS MathViewer
- by Heinrich P. Lotz and N. T. Peck PDF
- Proc. Amer. Math. Soc. 126 (1998), 75-84 Request permission
Abstract:
We prove that every separable Banach lattice is lattice isometric to a closed sublattice of the Banach envelope of Weak $L^{1}.$References
- Michael Cwikel and Charles Fefferman, Maximal seminorms on $\textrm {Weak}\,L^{1}$, Studia Math. 69 (1980/81), no.ย 2, 149โ154. MR 604347, DOI 10.4064/sm-69-2-149-154
- Michael Cwikel and Charles Fefferman, The canonical seminorm on weak $L^1$, Studia Math. 78 (1984), no.ย 3, 275โ278. MR 782664, DOI 10.4064/sm-78-3-275-278
- N. J. Kalton, Banach spaces embedding into $L_0$, Israel J. Math. 52 (1985), no.ย 4, 305โ319. MR 829361, DOI 10.1007/BF02774083
- J. Kupka and N. T. Peck, The $L_{1}$ structure of Weak $L^{1}$, Math. Ann. 269 (1984), 235-262.
- Heinrich P. Lotz, Extensions and liftings of positive linear mappings on Banach lattices, Trans. Amer. Math. Soc. 211 (1975), 85โ100. MR 383141, DOI 10.1090/S0002-9947-1975-0383141-7
- H. P. Lotz, $\text {Weak}^{\ast }$ convergence in the dual of Weak $L^{p}$, Israel J. Math. (to appear).
- H. P. Lotz, On the dual of the space Weak $L^{1}$.
- Heinrich P. Lotz and Haskell P. Rosenthal, Embeddings of $C(\Delta )$ and $L^{1}[0,\,1]$ in Banach lattices, Israel J. Math. 31 (1978), no.ย 2, 169โ179. MR 516253, DOI 10.1007/BF02760548
- N. T. Peck and Michel Talagrand, Banach sublattices of weak $L_1$, Israel J. Math. 59 (1987), no.ย 3, 257โ271. MR 920495, DOI 10.1007/BF02774140
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
- Received by editor(s): March 13, 1995
- Communicated by: Dale E. Alspach
- © Copyright 1998 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 126 (1998), 75-84
- MSC (1991): Primary 46B30, 46E30
- DOI: https://doi.org/10.1090/S0002-9939-98-03506-0
- MathSciNet review: 1343710