This is an announcement for the paper "Order continuous extensions of positive compact operators on Banach lattices" by Jin Xi Chen, Zi Li Chen and Guo Xing Ji.

Abstract: Let $E$ and $F$ be Banach lattices. Let $G$ be a vector sublattice of $E$ and $T: G\rightarrow F$ be an order continuous positive compact (resp. weakly compact) operators. We show that if $G$ is an ideal or an order dense sublattice of $E$, then $T$ has a norm preserving compact (resp. weakly compact) positive extension to $E$ which is likewise order continuous on $E$. In particular, we prove that every compact positive orthomorphism on an order dense sublattice of $E$ extends uniquely to a compact positive orthomorphism on $E$.

Archive classification: math.FA

Remarks: 7 pages

Submitted from: jinxichen@home.swjtu.edu.cn

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1102.4912

or

http://arXiv.org/abs/1102.4912