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The order boundedness of band preserving operators on uniformly complete vector lattices

Published online by Cambridge University Press:  24 October 2008

P. T. N. McPolin  and
A. W. Wickstead
P. T. N. McPolin
Affiliation:
The Queen's University of Belfast, BT7 1NN
A. W. Wickstead
Affiliation:
The Queen's University of Belfast, BT7 1NN
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Extract

1. Introduction. A linear operator T on a vector lattice is band preserving if x⊥ y implies Tx ⊥ y. Much is known about the order bounded band preserving operators on an Archimedean vector lattice. The collection of all of these forms an Abelian algebra under composition and a vector lattice for the operator order (see [7], [8] and [13] amongst others). Very little appears to be known about band preserving operators which are not order bounded apart from some isolated examples ([11], [13], [1] and [17]) and some non-existence results ([11] and [1]).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 97 , Issue 3 , May 1985 , pp. 481 - 487
Copyright
Copyright © Cambridge Philosophical Society 1985

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References

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