2014/12/09 by María J. Martín, Martín, María J., Jarno Talponen +1
Mathematics · #30H50 #30J05 #46J15 #47B33 #Advanced Operator Algebra Research #Advanced Topics in Algebra #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Operator Algebras (math.OA) #math.CV #math.FA #math.OA #msc:30H50 #msc:30J05 #msc:46J15 #msc:47B33
paper · pdf · doi:10.48550/arxiv.1412.3020
openalex publication_date 2014/12/09 · arxiv created 2015/01/22 · arxiv updated 2015/01/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The convex-transitivity property can be seen as a convex generalization of the almost transitive (or quasi-isotropic) group action of the isometry group of a Banach space on its unit sphere. We will show that certain Banach algebras, including conformal invariant Douglas algebras, are weak-star convex-transitive. Geometrically speaking, this means that the investigated spaces are highly symmetric. Moreover, it turns out that the symmetry property is satisfied by using only `inner' isometries, i.e. a subgroup consisting of isometries which are homomorphisms on the algebra. In fact, weighted composition operators arising from function theory on the unit disk will do. Some interesting examples are provided at the end.