Geodesic
Sur Les M-Ideaux Dans Certains Espaces D′Operateurs Et L′Approximation Par Des Operateurs Compacts
Canadian mathematical bulletin, Tome 23 (1980) no. 4, pp. 401-411

Voir la notice de l'article provenant de la source Cambridge University Press

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. 
Fakhoury, H. Sur Les M-Ideaux Dans Certains Espaces D′Operateurs Et L′Approximation Par Des Operateurs Compacts. Canadian mathematical bulletin, Tome 23 (1980) no. 4, pp. 401-411. doi: 10.4153/CMB-1980-059-3
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