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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

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