Previous |  Up |  Next


Banach space basic sequence copy of $c_{0}$ copy of $\ell _{\infty }$; basic sequence; copy of $c_{0}$; copy of $\ell _{\infty }$
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.
[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 1388616
[BP] C. Bessaga, A. Pełczyński: On bases and unconditional convergence of series in Banach spaces. Studia Math. 17 (1958), 151–164. DOI 10.4064/sm-17-2-151-164 | MR 0115069
[Di] J. Diestel: Sequences and Series in Banach Spaces. Springer-Verlag, New York Berlin Heidelberg Tokyo, 1984. MR 0737004
[Dr1] L. Drewnowski: Copies of $\ell _{\infty }$ in an operator space. Math. Proc. Cambridge Philos. Soc. 108 (1990), 523–526. DOI 10.1017/S0305004100069401 | MR 1068453
[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 10.1090/S0002-9939-1990-1012927-4 | MR 1012927
[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 1202755
[Em2] G. Emmanuele: On complemented copies of $c_{0}$ in spaces of compact operators, II. Commentat. Math. Univ. Carol. 35 (1994), 259–261. MR 1286572
[Fe1] J. C. Ferrando: When does $bvca\left( \Sigma ,X\right) $ contain a copy of $\ell _{\infty }$?. Math. Scand. 74 (1994), 271–274. MR 1298368
[Fe2] J. C. Ferrando: Copies of $c_{0}$ in certain vector-valued function Banach spaces. Math. Scand. 77 (1995), 148–152. DOI 10.7146/math.scand.a-12555 | MR 1365911
[Ka] N. J. Kalton: Spaces of compact operators. Math. Ann. 208 (1974), 267–278. DOI 10.1007/BF01432152 | MR 0341154 | Zbl 0266.47038
[Ro] H. P. Rosenthal: On relatively disjoint families of measures, with some applications to Banach space theory. Studia Math. 37 (1979), 13–36. DOI 10.4064/sm-37-1-13-36 | MR 0270122
Partner of
EuDML logo