2011/04/07 by Paul Bourdon, Bourdon, Paul, Wenling Shang +1
Mathematics · #47B32 #47B33 #Advanced Algebra and Geometry #Analytic and geometric function theory #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #math.FA #msc:47B32 #msc:47B33
paper · pdf · doi:10.48550/arxiv.1104.1329
14 pages
arxiv created 2011/04/07 · openalex publication_date 2011/04/07 · arxiv updated 2011/04/08 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28
We characterize those generating functions k that produce weighted Hardy spaces of the unit disk D supporting nontrivial Hermitian weighted composition operators. Our characterization shows that the spaces associated with the "classical reproducing kernels," as well as certain natural extensions of these spaces, are precisely those that are hospitable to Hermitian weighted composition operators. It also leads to a refinement of a necessary condition for a weighted composition to be Hermitian, obtained recently by Cowen, Gunatillake, and Ko, into one that is both necessary and sufficient.