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On positively complemented subspaces of c0

Published online by Cambridge University Press:  20 January 2009

Panayotis C. Tsekrekos
Panayotis C. Tsekrekos
Affiliation:
National Technical University of Athens42 Patission Street Athens 147, Greece
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It has been proved, see [1], that a closed infinite dimensional subspace of c0 is isomorphic to c0 if and only if it is the range of a bounded linear projection. In [6] we proved half of the order-theoretic analogue of this result. In fact we showed that an infinite dimensional subspace of c0 which is the range of a positive projection is order-isomorphic to c0. We left open the question whether the converse holds also true. In this paper we answer this question negatively by providing an example in Section 4. In Section 3 we give necessary and sufficient conditions in order that an ordered-subspace of c0 be the range of a positive projection.

Information

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 25 , Issue 1 , February 1982 , pp. 41 - 47
Copyright
Copyright © Edinburgh Mathematical Society 1982

References

REFERENCES

1.Pelzynski, A., Projections in certain Banach spaces, Studia Math. 19 (1960), 209–228.CrossRefGoogle Scholar
2.Fakhoury, H., Extensions uniformes des formes lineaires positives, Ann. Inst. Fourier, Grenoble 23 (1973), 75–94.CrossRefGoogle Scholar
3.Jameson, J. O., Ordered linear spaces Lecture Notes in Mathematics, 141, Springer-Verlag, Berlin, 1970).CrossRefGoogle Scholar
4.Jameson, J. O., Topology and normed spaces (Chapman and Hall, London, 1974).Google Scholar
5.Tsekrekos, P. C., Some applications of L-constants and M-constants on Banach Lattices, J. London Math. Soc. (2) 18 (1978), 133–139.CrossRefGoogle Scholar
6.Tsekrekos, P. C., Ordered-subspaces of some Banach lattices, J. London Math. Soc. (2) 18 (1978), 325–333.Google Scholar