Spaces of operators and $c_0$

P. Lewis¹

¹ Department of Mathematics University of North Texas Denton, TX 76203, U.S.A.

Studia Mathematica, Tome 145 (2001) no. 3, pp. 213-218

Résumé

Bessaga and Pełczyński showed that if $c_0$ embeds in the dual $X^*$ of a Banach space $X$, then $\ell ^1$ embeds complementably in $X$, and $\ell ^\infty $ embeds as a subspace of $X^*$. In this note the Diestel–Faires theorem and techniques of Kalton are used to show that if $X$ is an infinite-dimensional Banach space, $Y$ is an arbitrary Banach space, and $c_0$ embeds in $L(X,Y)$, then $\ell ^\infty $ embeds in $L(X,Y)$, and $\ell ^1$ embeds complementably in $X\otimes _{\gamma } Y^*$. Applications to embeddings of $c_0$ in various spaces of operators are given.

Détail

DOI : 10.4064/sm145-3-3

Keywords: bessaga czy ski showed embeds dual * banach space ell embeds complementably ell infty embeds subspace * note diestel faires theorem techniques kalton infinite dimensional banach space arbitrary banach space embeds ell infty embeds ell embeds complementably otimes gamma * applications embeddings various spaces operators given