On complemented copies of $c_0$ in spaces of operators, II
Emmanuele, Giovanni
Commentationes Mathematicae Universitatis Carolinae, Tome 35 (1994), p. 259-261 / Harvested from Czech Digital Mathematics Library

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 $Y$.

Publié le : 1994-01-01
Classification:  46A32,  46B20,  46B25,  46B28,  47D15
@article{118664,
     author = {Giovanni Emmanuele},
     title = {On complemented copies of $c\_0$ in spaces of operators, II},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {35},
     year = {1994},
     pages = {259-261},
     zbl = {0862.46010},
     mrnumber = {1286572},
     language = {en},
     url = {http://dml.mathdoc.fr/item/118664}
}
Emmanuele, Giovanni. On complemented copies of $c_0$ in spaces of operators, II. Commentationes Mathematicae Universitatis Carolinae, Tome 35 (1994) pp. 259-261. http://gdmltest.u-ga.fr/item/118664/

Bessaga C.; Pelczynski A On bases and unconditional convergence of series in Banach spaces, Studia Math. 17 (1958), 151-164. (1958) | MR 0115069 | Zbl 0084.09805

Diestel J. Sequences and Series in Banach Spaces, Graduate Text in Mathematics 97, Springer Verlag 1984. | MR 0737004

Emmanuele G. Dominated operators on $C[0,1]$ and the $(CRP)$, Collect. Math. 41 (1990), 21-25. (1990) | MR 1134442 | Zbl 0752.47006

Emmanuele G. Remarks on the uncomplemented subspace $W(E,F)$, J. Funct. Analysis 99 (1991), 125-130. (1991) | MR 1120917 | Zbl 0769.46006

Emmanuele G. On the containment of $c_0$ by spaces of compact operators, Bull. Sci. Math. 115 (1991), 177-184. (1991) | MR 1101022

Emmanuele G. A remark on the containment of $c_0$ in spaces of compact operators, Math. Proc. Cambridge Phil. Soc. 111 (1992), 331-335. (1992) | MR 1142753

Emmanuele G. On complemented copies of $c_0$ in spaces of operators, Comm. Math. 32 (1992), 29-32. (1992) | MR 1202755

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

Emmanuele G.; John K. Uncomplementability of spaces of compact operators in larger spaces of operators, to appear. | MR 1435603 | Zbl 0903.46006

Feder M. On subspaces of spaces with an unconditional basis and spaces of operators, Illinois J. Math. 34 (1980), 196-205. (1980) | MR 0575060 | Zbl 0411.46009

Holub J.R. Tensor product bases and tensor diagonals, Trans. Amer. Math. Soc. 151 (1970), 563-579. (1970) | MR 0279564 | Zbl 0216.16203

Kalton N.J. Spaces of compact operators, Math. Annalen 208 (1974), 267-278. (1974) | MR 0341154 | Zbl 0266.47038