Multiplication operators and dynamical systems on weighted spaces of vector-valued holomorphic functions on banach spaces

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Abstract

Let UX be a balanced open subset of a Banach space X. Let V and W be two Nachbin families of weights on UX. Let B(E, F) be the space of all continuous linear operators from a locally convex Haudorff space E into a locally convex Hausdorff space F. Let HV (UX, F) and HW (UX, E) be the weighted locally convex spaces of vector-valued holomorphic functions. In this paper, we investigate the operator-valued maps ψ: UX → B (E,F) which generate multiplication operators and invertible multiplication operators Mψ on the spaces HV (UX, F) and HW (UX, E) for general Nachbin families of weights V and W and for single continuous weights v and w on the open unit ball BX of a Banach space X. A C0-group of multiplication operators and a (linear) dynamical system is also obtained as an application of these operators.

Original languageEnglish
Pages (from-to)1075-1086
Number of pages12
JournalInternational Journal of Mathematical Analysis
Volume5
Issue number21-24
Publication statusPublished - 2011

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Keywords

  • C-group
  • Dynamical systems
  • Invertible multiplication operators
  • Multiplication operators
  • Nachbin families
  • Operated-valued holomorphic maps
  • Vector-valued holomorphic maps
  • Weighted locally convex spaces
  • Weights

ASJC Scopus subject areas

  • Mathematics(all)

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