Isometric weighted composition operators on weighted Banach spaces of holomorphic functions defined on the unit ball of a complex Banach space
Author
Wolf, Elke
Full text
https://revistas.ufro.cl/ojs/index.php/cubo/article/view/130810.4067/S0719-06462013000200004
Abstract
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.