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

Wong, Yau Chuen

doi:10.1090/S0002-9939-1975-0377464-0

On a theorem of Kōmura-Koshi and of Andô-Ellis
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Proc. Amer. Math. Soc. 52 (1975), 227-231 Request permission

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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