Note on compatible vector topologies

Kąkol, Jerzy

doi:10.1090/S0002-9939-1987-0877041-7

Note on compatible vector topologies
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by Jerzy Kąkol

Proc. Amer. Math. Soc. 99 (1987), 690-692

DOI: https://doi.org/10.1090/S0002-9939-1987-0877041-7

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Abstract:

Let $\left \langle {X,Y} \right \rangle$ be a dual pair. Then $X$ admits the finest locally convex topology $\mu$ which is compatible with $\left \langle {X,Y} \right \rangle$. In contrast, it is proved that there is no finest vector topology on $X$ which is compatible with $\left \langle {X,Y} \right \rangle$ provided $X$ contains a $\mu$-dense subspace of infinite codimension.

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