All Questions

Let $V$ be a real vector space. It is well known that a subset $B\subset V$ is the unit ball for some norm on $V$ if and only if $B$ satisfies the following conditions: $B$ is convex, i.e. if $v,w\...

Let $X$ be a locally convex topological space, and let $K \subset X$ be a compact set. Recalling that the standard convex hull is defined as $$\text{co}(K) = \Big\{ \sum_{i=1}^n a_i x_i : a_i \geq 0,\,...

Let $E$ be a Banach space. It is known that if for any equivalent norm on $E^*$ the closed unit ball of $E^*$ is weakly* closed, then $E$ is reflexive (a very short proof is in the book by Fabian, ...

Let $Y$ be a complemented subspace in a dual Banach space $X$. Is it true that $Y$ is itself isomorphic to a dual? This is the case of a $w^*$-closed subspace $Y$, but a complemented subspace of $X^*...