Quasi-Suslin weak duals

Abstract Cascales, Kakol, and Saxon (CKS) ushered Kaplansky and Valdivia into the grand setting of Cascales/Orihuela spaces E by proving: (K) If E is countably tight, then so is the weak space ( E , σ ( E , E ′ ) ) , and (V) ( E , σ ( E , E ′ ) ) is countably tight iff weak dual ( E ′ , σ ( E ′ , E ) ) is K-analytic . The ensuing flow of quasi-Suslin weak duals that are not K -analytic, a la Valdivia's example, continues here, where we argue that locally convex spaces E with quasi-Suslin weak duals are (K, V)'s best setting: largest by far, optimal vis-a-vis Valdivia. The vaunted CKS setting proves not larger, in fact, than Kaplansky's. We refine and exploit the quasi-LB strong dual interplay.