| Title:
|
$M$-ideals of compact operators into $\ell_p$ (English) |
| Author:
|
John, Kamil |
| Author:
|
Werner, Dirk |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
50 |
| Issue:
|
1 |
| Year:
|
2000 |
| Pages:
|
51-57 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We show for $2\le p<\infty $ and subspaces $X$ of quotients of $L_{p}$ with a $1$-unconditional finite-dimensional Schauder decomposition that $K(X,\ell _{p})$ is an $M$-ideal in $L(X,\ell _{p})$. (English) |
| MSC:
|
46B28 |
| MSC:
|
47B07 |
| MSC:
|
47L05 |
| idZBL:
|
Zbl 1040.46020 |
| idMR:
|
MR1745458 |
| . |
| Date available:
|
2009-09-24T10:29:50Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127547 |
| . |
| Reference:
|
[1] E. M. Alfsen and E. G. Effros: Structure in real Banach spaces. Parts I and II.Ann. of Math. 96 (1972), 98–173. MR 0352946, 10.2307/1970895 |
| Reference:
|
[2] P. G. Casazza and N. J. Kalton: Notes on approximation properties in separable Banach spaces.Geometry of Banach Spaces, Proc. Conf. Strobl 1989, P. F. X. Müller and W. Schachermayer (eds.), London Mathematical Society Lecture Note Series 158, Cambridge University Press, 1990, pp. 49–63. MR 1110185 |
| Reference:
|
[3] G. Godefroy, N. J. Kalton, and P. D. Saphar: Unconditional ideals in Banach spaces.Studia Math. 104 (1993), 13–59. MR 1208038 |
| Reference:
|
[4] P. Harmand, D. Werner, and W. Werner: $M$-Ideals in Banach Spaces and Banach Algebras.Lecture Notes in Math. 1547, Springer, Berlin-Heidelberg-New York, 1993. MR 1238713 |
| Reference:
|
[5] N. J. Kalton: $M$-ideals of compact operators.Illinois J. Math. 37 (1993), 147–169. Zbl 0824.46029, MR 1193134, 10.1215/ijm/1255987254 |
| Reference:
|
[6] N. J. Kalton and D. Werner: Property $(M)$, $M$-ideals and almost isometric structure of Banach spaces.J. Reine Angew. Math. 461 (1995), 137–178. MR 1324212 |
| Reference:
|
[7] A. Lima: Property $(wM^*)$ and the unconditional metric compact approximation property.Studia Math. 113 (1995), 249–263. Zbl 0826.46013, MR 1330210, 10.4064/sm-113-3-249-263 |
| Reference:
|
[8] D. Li: Complex unconditional metric approximation property for $C_\Lambda (\mathbf T)$ spaces.Preprint (1995). MR 1424701 |
| Reference:
|
[9] Ch. A. McCarthy: $c_p$.Israel J. Math. 5 (1967), 249–271. MR 0225140 |
| Reference:
|
[10] E. Oja: Dual de l’espace des opérateurs linéaires continus.C. R. Acad. Sc. Paris, Sér. A 309 (1989), 983–986. Zbl 0684.47025, MR 1054748 |
| Reference:
|
[11] D. Werner: New classes of Banach spaces which are $M$-ideals in their biduals.Math. Proc. Cambridge Phil. Soc. 111 (1992), 337–354. Zbl 0787.46020, MR 1142754, 10.1017/S0305004100075447 |
| . |
