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Sur Les M-Ideaux Dans Certains Espaces D′Operateurs Et L′Approximation Par Des Operateurs Compacts

Published online by Cambridge University Press:  20 November 2018

H. Fakhoury
H. Fakhoury*
Affiliation:
Equipe d′analyse Département de Mathématiques, Université de Paris VI, 2, Place Jussieu 75005-Paris.
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It is shown that if V=C(X) or V = L1(μ) then the subspace of compact (resp. weakly compact) operators from V into itself is not an M-ideal in the space of bounded operators. This is the contrary to what happens when V= Co(ℕ) or lp(ℕ). The main result is proved via the best approximation properties of M-ideals and some results concerning norm one projections in C(X) and L1(μ) are deduced from this fact.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 23 , Issue 4 , 01 December 1980 , pp. 401 - 411
Copyright
Copyright © Canadian Mathematical Society 1980

References

1. Alfsen, E. and Effros, E., Structure in real Banach spaces, Ann. of Math. 96 (1972), 98-173.Google Scholar
2. Amir, D. and Arbel, B., On injections and surjections in continuous function spaces, Israel J. Math. 15 (1973), 301-310.Google Scholar
3. Fakhoury, H., Existence d'une projection continue de meilleure approximation dans certains espaces de Banach, J. Math. Pures et Appl. 53 (1974), 1-16.Google Scholar
4. Grothendieck, A., Les applications linéaires faiblement compactes d'espaces de type C(X), Canad. J. Math. 5 (1953), 129-173.Google Scholar
5. Hennfeld, A., Decomposition for B(X) and unique Hahn-Banach extensions, Pacific J. Math. 46 (1973), 197-199.Google Scholar
6. Holmes, R., Scranton, B. and Ward, J., Approximation from the space of compact operators and other M-ideals, Duke Math. J. 42 (1975), 259-269.Google Scholar
7. Mach, J. and Ward, J., Approximation by compact operators on certain Banach spaces, J. Approximation theory (à paraître).Google Scholar
8. Wulbert, D., Projections of norm 1 on C(X), Notices Amer. Math. Soc. 15 (1968), 362.Google Scholar
9. Daugavet, A., A property of completely continuous functions on the space C, Uspehi Math. Nauk. 18 (1963), 157-158.Google Scholar