✍ Scribed by Stephen A. Saxon; Ian Tweddle
No coin nor oath required. For personal study only.
In the context of Reinventing weak barrelledness,'' the best possible versions of the Robertson Saxon Robertson Splitting Theorem and the Saxon Tweddle Fit and Flat Components Theorem are obtained by weakening the hypothesis from barrelled'' to Mackey and + 0 -barreled.'' An example showing that the latter does not imply the former validates novelty, answers an old question, and completes a robust linear picture of Mackey weak barrelledness'' begun several decades ago.
📜 SIMILAR VOLUMES
A HAUSDORFF locally convex space is said to be c,-barrelled (respectively cu-barrelled) if each sequence in the dual space t h a t converges weakly to 0 (res!,r:ctively t h a t is weakly ?.~oundecl), is equicontinuous. It is proved that if a c,,-barrelled space E has dual E' weakly sequentially comp
Let X be a completely regular Hausdorff space, let E be a normed space, let C X E C X if E is scalars) be the space of all E-valued continuous functions on X, and let L X be the vector space of discrete measures on X. There is a natural duality between L X and C X . In this paper the completion of t