Let X and Y be complex Banach spaces and BX resp. BY the closed unit ball. Analytic maps φ : BY → BX and ψ : BX → C induce the weighted composition operator:
Cφ,ψ : H(BY) → H(BX), f → ψ(f ◦ φ),
where H(BY) resp. H(BX) denotes the collection of all analytic functions f : BX(resp.BY) → C. We study when such operators acting between weighted spaces of analytic functions are isometric.
@article{1308,
title = {Isometric weighted composition operators on weighted Banach spaces of holomorphic functions defined on the unit ball of a complex Banach space},
journal = {CUBO, A Mathematical Journal},
volume = {15},
year = {2013},
language = {en},
url = {http://dml.mathdoc.fr/item/1308}
}
Wolf, Elke. Isometric weighted composition operators on weighted Banach spaces of holomorphic functions defined on the unit ball of a complex Banach space. CUBO, A Mathematical Journal, Tome 15 (2013) . http://gdmltest.u-ga.fr/item/1308/