Isometric weighted composition operators on weighted Banach spaces of holomorphic functions defined on the unit ball of a complex Banach space

Elke Wolf

doi:10.4067/S0719-06462013000200004

Isometric weighted composition operators on weighted Banach spaces of holomorphic functions defined on the unit ball of a complex Banach space

Authors

Elke Wolf University of Paderborn, Mathematical Institute, D-33095 Paderborn, Germany.

DOI:

https://doi.org/10.4067/S0719-06462013000200004

Keywords:

weighted composition operators, weighted spaces of holomorphic functions on the unit ball of a complex Banach space

Abstract

Let X and Y be complex Banach spaces and B_X resp. B_Y the closed unit ball. Analytic maps Ï† : B_Y â†’ B_X and Ïˆ : B_X â†’ C induce the weighted composition operator:

C_Ï†,Ïˆ : H(B_Y) â†’ H(B_X), f â†’ Ïˆ(f â—¦ Ï†),

where H(B_Y) resp. H(B_X) denotes the collection of all analytic functions f : B_X(resp.B_Y) â†’ C. We study when such operators acting between weighted spaces of analytic functions are isometric.

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Published

2013-06-01

How to Cite

[1]

E. Wolf, “Isometric weighted composition operators on weighted Banach spaces of holomorphic functions defined on the unit ball of a complex Banach space”, CUBO, vol. 15, no. 2, pp. 43–52, Jun. 2013.