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A Banach lattice not weakly projectable

Published online by Cambridge University Press:  09 April 2009

E. Strzelecki
E. Strzelecki
Affiliation:
Department of Mathematics, Monash University, Victoria 3168, Australia
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In [4] a concept of a weakly projectable vector lattice has been introduced. Stone vector lattices [3] and thus all special types of them, like Riesz [5], σ-complete and complete vector lattices are weakly projectable. Moreover C[0, 1] is weakly projectable but not Stone [4]. As we see the collection W of weakly projectable vector lattices is quite large. This explains to some extent the difficulty in producing examples of vector lattices which do not belong to W. In this note an example of a Banach lattice [1] which is not weakly projectable is described.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 18 , Issue 1 , August 1974 , pp. 76 - 77
Copyright
Copyright © Australian Mathematical Society 1974

References

[1]Birkhoff, G., Lattice theory (American Mathematical Society, Providence 1967, Colloquium publication 25).Google Scholar
[2]Peressini, A. L., Ordered topological vector spaces (Harper's Series in Modern Mathematics, 1967).Google Scholar
[3] T. P. Speed, ‘On commutative l-groups’, (to appear)Google Scholar
[4]Spirason, G. T. and Strzelecki, E. ‘A note on Pt-ideals’, J. Austral. Math. Soc., 14 (1972), 304–310.CrossRefGoogle Scholar
[5]Vulikh, B. Z., Introduction to the theory of partially ordered spaces. (Wolters-Noordhoff Scientific Publications, Groningen, 1967).Google Scholar