Weighted composition operators and dynamical systems on weighted spaces of holomorphic functions on banach spaces

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Abstract

Let BX and BY be the open unit balls of the Banach Spaces X and Y , respectively. Let V and W be two countable families of weights on BX and BY , respectively. Let HV (BX) (or HV0 (BX)) and HW (BY) (or HW0 (BY)) be the weighted Fréchet spaces of holomorphic functions. In this paper, we investigate the holomorphic mappings φ : BX → BY and Ψ: BX → C which characterize continuous weighted composition operators between the spaces HV (BX) (or HV0 (BX)) and HW (BY) (or HW0 (BY)) : Also, we obtained a (linear) dynamical system induced by multiplication operators on these weighted spaces.

Original languageEnglish
Pages (from-to)58-71
Number of pages14
JournalAnnals of Functional Analysis
Volume4
Issue number2
Publication statusPublished - 2013

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Keywords

  • Dynamical system
  • Multiplication operator.
  • Weight
  • Weighted composition operator
  • Weighted frechet space

ASJC Scopus subject areas

  • Analysis
  • Control and Optimization

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