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On a theorem of Kōmura-Koshi and of Andô-Ellis


Author: Yau Chuen Wong
Journal: Proc. Amer. Math. Soc. 52 (1975), 227-231
MSC: Primary 46A40
DOI: https://doi.org/10.1090/S0002-9939-1975-0377464-0
MathSciNet review: 0377464
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Abstract: Kōmura and Koshi’s result, which states that the topology $\mathcal {I}$ of a nuclear locally convex vector lattice $(E,C,\mathcal {I})$ is the topology $o(E,E’)$ of uniform convergence on all order-intervals in $E’$, is generalized to the case when $(E,C,\mathcal {I})$ is only a locally solid space. Andô-Ellis’ theorem, concerning the duality of strict $\mathfrak {B}$-cones and normality in normed vector spaces, is generalized to the metrizable case.


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Keywords: Solid, order-convex, decomposable, nuclear, base norm, strict <!– MATH $\mathfrak {B}$ –> <IMG WIDTH="23" HEIGHT="21" ALIGN="BOTTOM" BORDER="0" SRC="images/img2.gif" ALT="$\mathfrak {B}$">-cones, normal cones, open decomposition, locally solid spaces, locally decomposable spaces, locally <IMG WIDTH="16" HEIGHT="20" ALIGN="BOTTOM" BORDER="0" SRC="images/img1.gif" ALT="$o$">-convex spaces
Article copyright: © Copyright 1975 American Mathematical Society