2024/02/22 by Isabelle Chalendar, Chalendar, I., Luc Oger +3 · 1 citation
Mathematics · #Holomorphic and Operator Theory #Algebraic and Geometric Analysis #Analytic and geometric function theory
paper · pdf · doi:10.48550/arxiv.2402.14671
A complete characterisation is given of all the linear isometries of the Fréchet space of all holomorphic functions on the unit disc, when it is given one of the two standard metrics: these turn out to be weighted composition operators of a particular form. Operators similar to an isometry are also classified. Further, the larger class of operators isometric when restricted to one of the defining seminorms is identified. Finally, the spectra of such operators are studied.