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

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DOI:

https://doi.org/10.4067/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 â—¦ 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.

Keywords

weighted composition operators , weighted spaces of holomorphic functions on the unit ball of a complex Banach space
  • Elke Wolf University of Paderborn, Mathematical Institute, D-33095 Paderborn, Germany.
  • Pages: 43–52
  • Date Published: 2013-06-01
  • Vol. 15 No. 2 (2013): CUBO, A Mathematical Journal

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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.

Issue

Vol. 15 No. 2 (2013): CUBO, A Mathematical Journal

Section

Articles