This is an announcement for the paper "A version of Kalton's theorem for the space of regular operators" by Foivos Xanthos.
Abstract: In this note we extend some recent results in the space of regular operators. In particular, we provide the following Banach lattice version of a classical result of Kalton: Let $E$ be an atomic Banach lattice with an order continuous norm and $F$ a Banach lattice. Then the following are equivalent: (i) $L^r(E,F)$ contains no copy of $\ell_\infty$, ,, (ii) $L^r(E,F)$ contains no copy of $c_0$, ,, (iii) $K^r(E,F)$ contains no copy of $c_0$, ,, (iv) $K^r(E,F)$ is a (projection) band in $L^r(E,F)$, ,, (v) $K^r(E,F)=L^r(E,F)$.
Archive classification: math.FA
Submitted from: foivos@ualberta.ca
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1310.1591
or