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Complemented subspaces and the Hahn-Banach extension property in lp(0 < p < 1)

Published online by Cambridge University Press:  18 May 2009

M. A. Ariño  and
M. A. Canela
M. A. Ariño
Affiliation:
Department of Mathematical Analysis, University of Barcelona, Gran Via 585, Barcelona 08007, Spain
M. A. Canela
Affiliation:
Department of Mathematical Analysis, University of Barcelona, Gran Via 585, Barcelona 08007, Spain
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In this article, we study some questions related to the complementation and the Hahn-Banach property for subspaces of lp, for 0 < p < 1. Some results which are stated here have appeared in the work of W. J. Stiles [4, 5] and N. Popa [3], but our proofs are simpler. We solve a problem raised by Popa [3], concerning complemented copies of lp contained in lp.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 28 , Issue 2 , July 1986 , pp. 115 - 120
Copyright
Copyright © Glasgow Mathematical Journal Trust 1986

References

REFERENCES

1.Köthe, G., Topological Vector Spaces I (Springer, 1969).Google Scholar
2.Lindenstrauss, J. and Tzafriri, L., Classical Banach Spaces I (Springer, 1977).CrossRefGoogle Scholar
3.Popa, N., On complemented subspaces of lp, 0<p<1, Rev. Roumaine Math. Pures Appl. 26 (1981), 287–299.Google Scholar
4.Stiles, W. J., On properties of subspaces of lp,0<p< 1, Trans. Amer. Math. Soc. 149 (1970), 405–415.Google Scholar
5.Stiles, W. J.. Some properties of l p, 0<p<1. Studia Math. 42 (1972), 109–119.Google Scholar