Geodesic
M-Ideals in L(l1, E)
Canadian mathematical bulletin, Tome 29 (1986) no. 1, pp. 3-10

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In this article it is shown that for any Banach space E,L (l1,E) always contains uncountably many distinct A/-ideals that are closed subspaces of K(l1,E) and which are not complemented in L (l1,E) . Using standard duality arguments one obtains the result that infinitely many distinct subspaces of K(E, c0) are M-ideals in L(E, c0). In particular, for the case E = c0, this shows that the uniqueness conditions enjoyed by K(lp), p > 1, is not valid for E = c0. The results are obtained by utilizing the identification of L (l1,E) with the vector-valued sequence space lx(E) and to exploit natural decompositions of lx(E)’ afforded by a class of Lprojections on lx(E)’ induced by certain E'-valued vector measures.
DOI : 10.4153/CMB-1986-001-5
Mots-clés : Primary 46B20, Secondary 46A32 
Fleming, D. J.; Giarrusso, D. M. M-Ideals in L(l1, E). Canadian mathematical bulletin, Tome 29 (1986) no. 1, pp. 3-10. doi: 10.4153/CMB-1986-001-5
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[1] 1. Alfsen, E. M. and Effros, E. G., Structure in real Banach spaces I, Ann. of Math., 96 (1972), pp. 98–173. Google Scholar

[2] 2. Behrends, E., et al., U structure in real Banach spaces, 613, Springer Lecture Notes. Google Scholar

[3] 3. Behrends, E., “M structure and the Banach Stone Theorem ” 736, Springer Lecture Notes. Google Scholar

[4] 4. Cunningham, F., L-structures in L-spaces, Trans. Amer. Math. Soc, 95 (1960), pp. 274—299. Google Scholar

[5] 5. Dixmier, J, Les fonctionnelles linéaires sur l’ ensembles des opérateurs bornés d'un espace de Hubert, Ann. of Math, 51 (1950), pp. 387–408. Google Scholar

[6] 6. Fleming, D. J. and Giarrusso, D. M., Topological decompositions of the duals of locally convex operator spaces, Math. Proc. Camb. Phil. Soc, 93 (1983), pp. 307–314. Google Scholar

[7] 7. Flynn, P., A characterization of M-ideals in B(l)for J < p < ∞, pac . J. Math, 98 (1982), pp. 73–80. Google Scholar

[8] 8. Hennefeld, J. A., A decomposition for B(X)* and unique Hahn—Banach extensions, Pac. J. Math, 46 (1973), pp. 197–199. Google Scholar

[9] 9. Mach, J. and Ward, J., Approximation by compact operators on certain Banach spaces, J. Approximation Theory, 23 (1978), pp. 274–286. Google Scholar

[10] 10. Saatkamp, K., M-ideals of compact operators, Math. Z., 158 (1978), pp. 253–263. Google Scholar

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