A Note on M-Ideals of Compact operators
Canadian mathematical bulletin, Tome 32 (1989) no. 4, pp. 434-440

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

Suppose X and Y are closed subspaces of (ΣXn)p and (ΣYn)q (1 < p ≦ q < ∞, dim Xn < ∞, dimYn < ∞), respectively. If K(X, Y), the space of the compact linear operators from X to Y, is dense in L(X, Y), the space of the bounded linear operators from X to Y, in the strong operator topology, then K(X, Y) is an M-ideal in L(X, Y).
DOI : 10.4153/CMB-1989-062-8
Mots-clés : 46A32, 47B05, 47B05, 41A50, Compact operators, M-ideal, finite dimensional decomposition, strong operator topology, compact approximation property
Cho, Chong-Man. A Note on M-Ideals of Compact operators. Canadian mathematical bulletin, Tome 32 (1989) no. 4, pp. 434-440. doi: 10.4153/CMB-1989-062-8
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[1] 1. Alfsen, E. M. and E. G. Effros, Structure in real Banach spaces, Ann. of Math. 96 (1972), 98–173. Google Scholar

[2] 2. Behrends, E., M-structure and the Banach-Stone Theorem, Lecture Note in Mathematics 736, Springer-Verlag (1979). Google Scholar

[3] 3. Cho, C.-M. and Johnson, W. B., A characterization of sub space s X of lp for which K(X) is an M-ideal in L﹛X), Proc. Amer. Math. Soc. 93 (1985), 466–470. Google Scholar

[4] 4. Cho, C.-M., M-ideals of compact operators, Pacific J. Math, 138 (1989), 237–242. Google Scholar

[5] 5. Harmand, P. and Lima, A., Banach spaces which are M-ideals in their biduals, Trans. Amer. Math. Soc. 283 (1983), 253–264. Google Scholar

[6] 6. Hennefeld, J., A decomposition for B(X)* and unique Hahn-Banach extensions, Pacific J. Math. 46 (1973), 197–199. Google Scholar

[7] 7. Lima, A., Intersection properties of balls and subspaces of Banach spaces, Trans. Amer. Math. Soc. 227 (1977), 1–62. Google Scholar

[8] 8. Lima, A., Intersection properties of balls in the space of compact operators, Ann. Inst. Fourier, Grenoble 28, 3 (1978), 274–286. Google Scholar

[9] 9. Lima, A., M-ideals of compact operators in classical Banach spaces, Math. Scand. 44 (1979), 207- 217. Google Scholar

[10] 10. Lindenstrauss, J. and Tzafriri, L., Classical Banach spaces I, Springer-Verlag, Berlin (1977). Google Scholar

[11] 11. March, J. and Ward, J. D., Approximation by compact operators on certain Banach spaces, J. of Approximaion theory 23 (1978), 274–284. Google Scholar

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

[13] 13. Smith, R. R. and Ward, J. D., M-ideal structure in Banach algebras, J. Func. Anal. 27 (1978), 337–349. Google Scholar

[14] 14. Smith, R. R. and J. D. Ward, Application of convexity and M-ideal theory to quotient Banach algebras, Quart. J. Math. Oxford (2), 30 (1979), 365–384. Google Scholar

[15] 15. Werner, D., Remarks on M-ideals of compact operators, preprint. Google Scholar

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