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|Title:||The classification problem for nonatomic weak Lp spaces|
|Authors:||Leung, D.H. |
|Keywords:||Isomorphism of Banach spaces|
Weak Lp spaces
|Citation:||Leung, D.H., Sabarudin, R. (2010-01-15). The classification problem for nonatomic weak Lp spaces. Journal of Functional Analysis 258 (2) : 373-396. ScholarBank@NUS Repository. https://doi.org/10.1016/j.jfa.2009.08.001|
|Abstract:||The aim of the paper is to study the isomorphic structure of the weak Lp space Lp, ∞ (Ω, Σ, μ) when (Ω, Σ, μ) is a purely nonatomic measure space. Using Maharam's classification of measure algebras, it is shown that every such Lp, ∞ (Ω, Σ, μ) is isomorphic to a weak Lp space defined on a weighted direct sum of product measure spaces of the type 2κ. Several isomorphic invariants are then obtained. In particular, it is found that there is a notable difference between the case 1 < p < 2 and the case where 2 ≤ p < ∞. Applying the methods developed, we obtain an isomorphic classification of the purely nonatomic weak Lp spaces in a special case. © 2009 Elsevier Inc. All rights reserved.|
|Source Title:||Journal of Functional Analysis|
|Appears in Collections:||Staff Publications|
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