Sequential and Conditional Compactness in the Dual of a Barrelled Space
Sequential and Conditional Compactness in the Dual of a Barrelled Space
Let $E$ be a barrelled locally convex space and suppose ${T_{\mathcal {A}}}$ is a topology on the dual $Eâ$ of $E$ which is admissible for the duality $(E,Eâ)$. It is shown that each ${T_{\mathcal {A}}}$ sequentially compact subset of $Eâ$ is ${T_{\mathcal {A}}}$ conditionally compact.