2015/06/22 by Christopher Boyd, Pilar Rueda, Boyd, Christopher +1
Mathematics · #Advanced Topics in Algebra #Algebraic and Geometric Analysis #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #math.FA
paper · pdf · doi:10.48550/arxiv.1506.06532
arxiv created 2015/06/22 · openalex publication_date 2015/06/22 · arxiv updated 2015/06/23 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
We examine the surjectivity of isometries between weighted spaces of holomorphic functions. We show that for certain classical weights on the open unit disc all isometries of the weighted space of holomorphic functions, \mathcal Hvo( Δ), are surjective. Criteria for surjectivity of isometries of \mathcal Hv(U) in terms of a separation condition on points in the image of \mathcal Hvo(U) are also given for U a bounded open set in ℂ. Considering the weight v(z)= 1-|z|2 and the isomorphism f↦ f' we are able to show that all isometries of the little Bloch space are surjective.