Linear isometries of Hol(D) - Archive ouverte HAL
Journal Articles Journal of Mathematical Analysis and Applications Year : 2024

Linear isometries of Hol(D)

Abstract

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.
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Dates and versions

hal-04473335 , version 1 (22-02-2024)

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Cite

Isabelle Chalendar, Lucas Oger, J.R. Partington. Linear isometries of Hol(D). Journal of Mathematical Analysis and Applications, 2024, 540 (1), pp.128619. ⟨10.1016/j.jmaa.2024.128619⟩. ⟨hal-04473335⟩
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