Electronic Resource
Springer
Manuscripta mathematica
33 (1981), S. 217-226
ISSN:
1432-1785
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract The criterion of Dunford-Pettis for weak compactness in Banach lattices of L1(μ) type can be derived from a characterisation of weak sequentially complete topological vector lattices. This can be done by introducing a concept which reduces to uniform integrability in the L1(μ) case ([1], [8]). In other cases suitable choice of the topology leads to definitions given by [4], [9], [11] and [12]. It is shown in this paper that the orthogonally compact subsets of a Banach lattice are characterized as those relatively weakly compact sets on which the norm and the order topology agree.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01798227
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