arXiv subjects
Publications and source records attributed to Ikhan Choi.
We construct a subadditive weight on the type I$_\infty$ factor that preserves directed suprema but is not $\sigma$-weakly lower semi-continuous. This provides a counterexample to Haagerup's first problem posed in 1975.
We affirmatively resolve a question posed by Uffe Haagerup in 1975 on the positive version of the bipolar theorem on the dual spaces of C$^*$-algebras. As a direct consequence, we obtain a complete set of four positive Hahn-Banach separation theorems on von Neumann algebras, their preduals, C$^*$-algebras, and their duals. Furthermore, with the idea used to solve the problem, we simplify Haagerup's original solution to Dixmier's problem on normal weights.