| Title:
|
On complemented copies of $c_0$ in spaces of operators, II (English) |
| Author:
|
Emmanuele, Giovanni |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
35 |
| Issue:
|
2 |
| Year:
|
1994 |
| Pages:
|
259-261 |
| . |
| Category:
|
math |
| . |
| Summary:
|
We show that as soon as $c_0$ embeds complementably into the space of all weakly compact operators from $X$ to $Y$, then it must live either in $X^\ast$ or in $Y$. (English) |
| Keyword:
|
spaces of weakly compact operators |
| Keyword:
|
complemented copies of $c_0$ |
| MSC:
|
46A32 |
| MSC:
|
46B20 |
| MSC:
|
46B25 |
| MSC:
|
46B28 |
| MSC:
|
47D15 |
| idZBL:
|
Zbl 0862.46010 |
| idMR:
|
MR1286572 |
| . |
| Date available:
|
2009-01-08T18:10:45Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118664 |
| . |
| Reference:
|
[BP] Bessaga C., Pelczynski A: On bases and unconditional convergence of series in Banach spaces.Studia Math. 17 (1958), 151-164. Zbl 0084.09805, MR 0115069 |
| Reference:
|
[D] Diestel J.: Sequences and Series in Banach Spaces.Graduate Text in Mathematics 97, Springer Verlag 1984. MR 0737004 |
| Reference:
|
[E1] Emmanuele G.: Dominated operators on $C[0,1]$ and the $(CRP)$.Collect. Math. 41 (1990), 21-25. Zbl 0752.47006, MR 1134442 |
| Reference:
|
[E2] Emmanuele G.: Remarks on the uncomplemented subspace $W(E,F)$.J. Funct. Analysis 99 (1991), 125-130. Zbl 0769.46006, MR 1120917 |
| Reference:
|
[E3] Emmanuele G.: On the containment of $c_0$ by spaces of compact operators.Bull. Sci. Math. 115 (1991), 177-184. MR 1101022 |
| Reference:
|
[E4] Emmanuele G.: A remark on the containment of $c_0$ in spaces of compact operators.Math. Proc. Cambridge Phil. Soc. 111 (1992), 331-335. MR 1142753 |
| Reference:
|
[E5] Emmanuele G.: On complemented copies of $c_0$ in spaces of operators.Comm. Math. 32 (1992), 29-32. MR 1202755 |
| Reference:
|
[E6] Emmanuele G.: About the position of $K_{w^\ast}(X^\ast,Y)$ in $L_{w^\ast}(X^\ast,Y)$.Atti Sem. Mat. Fisico Univ. Modena, to appear. MR 1282327 |
| Reference:
|
[EJ] Emmanuele G., John K.: Uncomplementability of spaces of compact operators in larger spaces of operators.to appear. Zbl 0903.46006, MR 1435603 |
| Reference:
|
[F] Feder M.: On subspaces of spaces with an unconditional basis and spaces of operators.Illinois J. Math. 34 (1980), 196-205. Zbl 0411.46009, MR 0575060 |
| Reference:
|
[H] Holub J.R.: Tensor product bases and tensor diagonals.Trans. Amer. Math. Soc. 151 (1970), 563-579. Zbl 0216.16203, MR 0279564 |
| Reference:
|
[K] Kalton N.J.: Spaces of compact operators.Math. Annalen 208 (1974), 267-278. Zbl 0266.47038, MR 0341154 |
| . |
