Linear isometries of Hol(D)
Complex Variables
2024-05-17 v2
Abstract
A complete characterisation is given of all the linear isometries of the Fr\'echet 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.
Cite
@article{arxiv.2402.14671,
title = {Linear isometries of Hol(D)},
author = {I. Chalendar and L. Oger and J. R. Partington},
journal= {arXiv preprint arXiv:2402.14671},
year = {2024}
}
Comments
19 pages