Convex Transitive Norms on Spaces of Continuous Functions

摘要: A norm on a Banach space $X$ is called maximal when no equivalent has larger group of isometries. If, besides this, there with the same isometries (apart from its scalar multiples), said to be uniquely maximal, which convex-transitivity : convex hull orbits under action isometry unit sphere dense in ball . The main result paper that complex $C_0(\Omega)$ convex-transitive natural supremum if $\Omega$ connected manifold (without boundary). As complement, it shown dimension at least two, then diameter transitive corresponding real functions.