Vector lattices of weakly compact operators on Banach lattices
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- by Z. L. Chen and A. W. Wickstead PDF
- Trans. Amer. Math. Soc. 352 (2000), 397-412 Request permission
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.References
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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
- MR Author ID: 182585
- Email: A. Wickstead@qub.ac.uk
- Received by editor(s): May 7, 1997
- Published electronically: July 21, 1999
- © Copyright 1999 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 352 (2000), 397-412
- MSC (1991): Primary 47B65; Secondary 47B07
- DOI: https://doi.org/10.1090/S0002-9947-99-02431-9
- MathSciNet review: 1641095