Order continuous extensions of positive compact operators on Banach lattices

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 $E$.Comment: 7 page

Controlling the Intrinsic Josephson Junction Number in a Bi2Sr2CaCu2O8+δ\mathbf{Bi_2Sr_2CaCu_2O_{8+\delta}} Mesa

In fabricating $\mathrm{Bi_2Sr_2CaCu_2O_{8+\delta}}$ intrinsic Josephson junctions in 4-terminal mesa structures, we modify the conventional fabrication process by markedly reducing the etching rates of argon ion milling. As a result, the junction number in a stack can be controlled quite satisfactorily as long as we carefully adjust those factors such as the etching time and the thickness of the evaporated layers. The error in the junction number is within $\pm 1$. By additional ion etching if necessary, we can controllably decrease the junction number to a rather small value, and even a single intrinsic Josephson junction can be produced.Comment: to bu published in Jpn. J. Appl. Phys., 43(7A) 200