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:
https://doi.org/10.1090/S0002-9947-99-02431-9

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