Abstract of a paper by Jin Xi Chen, Zi Li Chen and Guo Xing Ji
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
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