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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Vector lattices of weakly compact operators
on Banach lattices


Authors: Z. L. Chen and A. W. Wickstead
Journal: Trans. Amer. Math. Soc. 352 (2000), 397-412
MSC (1991): Primary 47B65; Secondary 47B07
Published electronically: July 21, 1999
MathSciNet review: 1641095
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Abstract: A result of Aliprantis and Burkinshaw shows that weakly compact operators from an AL-space into a KB-space have a weakly compact modulus. Groenewegen characterised the largest class of range spaces for which this remains true whenever the domain is an AL-space and Schmidt proved a dual result. Both of these authors used vector-valued integration in their proofs. We give elementary proofs of both results and also characterise the largest class of domains for which the conclusion remains true whenever the range space is a KB-space. We conclude by studying the order structure of spaces of weakly compact operators between Banach lattices to prove results analogous to earlier results of one of the authors for spaces of compact operators.


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Additional Information

Z. L. Chen
Affiliation: Department of Applied Mathematics, Southwest Jiaotong University, Chengdu Sichuan 610031, People’s Republic of China

A. W. Wickstead
Affiliation: Department of Pure Mathematics, The Queen’s University of Belfast, Belfast BT7 1NN, Northern Ireland
Email: A. Wickstead@qub.ac.uk

DOI: http://dx.doi.org/10.1090/S0002-9947-99-02431-9
PII: S 0002-9947(99)02431-9
Keywords: Weakly compact operators, Banach lattices
Received by editor(s): May 7, 1997
Published electronically: July 21, 1999
Article copyright: © Copyright 1999 American Mathematical Society