Matrix maps and the isomorphic structure of BK spaces

Abstract

This note gives a characterization of BK spaces that contain isomorphic copies of c 0 {c_0} in terms of matrix maps and a sufficient condition for a matrix map from l ∞ {l_\infty } into a BK space to be a compact operator. The primary tool used in this note is the Bessaga-Pelczynski characterization of Banach spaces which contain isomorphic copies of c 0 {c_0} . It is shown that weakly compact matrix maps on l ∞ {l_\infty } are compact and that, if E E is a BK space such that there is a matrix A A such that c 0 ⊆ E A {c_0} \subseteq {E_A} and E A {E_A} is not strongly conull, then E E must contain an isomorphic copy of c 0 {c_0} .