On copies of $c_0$ in the bounded linear operator space
Czechoslovak Mathematical Journal, Tome 50 (2000) no. 3, pp. 651-656

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In this note we study some properties concerning certain copies of the classic Banach space $c_{0}$ in the Banach space $\mathcal{L}\left( X,Y\right) $ of all bounded linear operators between a normed space $X$ and a Banach space $Y$ equipped with the norm of the uniform convergence of operators.
In this note we study some properties concerning certain copies of the classic Banach space $c_{0}$ in the Banach space $\mathcal{L}\left( X,Y\right) $ of all bounded linear operators between a normed space $X$ and a Banach space $Y$ equipped with the norm of the uniform convergence of operators.
Classification : 46B03, 46B25, 46B28, 46E40
Keywords: Banach space basic sequence copy of $c_{0}$ copy of $\ell _{\infty }$; basic sequence; copy of $c_{0}$; copy of $\ell _{\infty }$
Ferrando, J. C.; Amigó, J. M. On copies of $c_0$ in the bounded linear operator space. Czechoslovak Mathematical Journal, Tome 50 (2000) no. 3, pp. 651-656. http://geodesic.mathdoc.fr/item/CMJ_2000_50_3_a16/
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     title = {On copies of $c_0$ in the bounded linear operator space},
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     year = {2000},
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     zbl = {1079.46512},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2000_50_3_a16/}
}
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[BDL] J. Bonet, P. Domaǹski, Å. Lindström: Cotype and complemented copies of $c_{0}$ in spaces of operators. Czechoslovak Math. J. 46 (1996), 271–289. | MR

[BP] C. Bessaga, A. Pełczyński: On bases and unconditional convergence of series in Banach spaces. Studia Math. 17 (1958), 151–164. | DOI | MR

[Di] J. Diestel: Sequences and Series in Banach Spaces. Springer-Verlag, New York Berlin Heidelberg Tokyo, 1984. | MR

[Dr1] L. Drewnowski: Copies of $\ell _{\infty }$ in an operator space. Math. Proc. Cambridge Philos. Soc. 108 (1990), 523–526. | DOI | MR

[Dr2] L. Drewnowski: When does $ca\left( \Sigma ,X\right) $ contain a copy of $\ell _{\infty }$ or $c_{0}$?. Proc. Amer. Math. Soc. 109 (1990), 747–752. | DOI | MR

[Em] G. Emmanuele: On complemented copies of $c_{0}$ in spaces of compact operators. Ann. Soc. Math. Pol., Ser. I, Commentat. Math. 32 (1992), 29–32. | MR

[Em2] G. Emmanuele: On complemented copies of $c_{0}$ in spaces of compact operators, II. Commentat. Math. Univ. Carol. 35 (1994), 259–261. | MR

[Fe1] J. C. Ferrando: When does $bvca\left( \Sigma ,X\right) $ contain a copy of $\ell _{\infty }$?. Math. Scand. 74 (1994), 271–274. | MR

[Fe2] J. C. Ferrando: Copies of $c_{0}$ in certain vector-valued function Banach spaces. Math. Scand. 77 (1995), 148–152. | DOI | MR

[Ka] N. J. Kalton: Spaces of compact operators. Math. Ann. 208 (1974), 267–278. | DOI | MR | Zbl

[Ro] H. P. Rosenthal: On relatively disjoint families of measures, with some applications to Banach space theory. Studia Math. 37 (1979), 13–36. | DOI | MR