CONVEX-TRANSITIVE DOUGLAS ALGEBRAS

摘要: The convex-transitivity property can be seen as a convex generalization of the almost transitive (or quasi-isotropic) group action isometry Banach space on its unit sphere. We will show that certain algebras, including conformal invariant Douglas are weak-star convex-transitive. Geometrically speaking, this means investigated spaces highly symmetric. Moreover, it turns out symmetry is satisfied by using only 'inner' isometries, i.e. subgroup consisting isometries which homomorphisms algebra. In fact, weighted composition operators arising from function theory disk do. Some interesting examples provided at end.