Compact differences of weighted composition operators on weighted banach spaces of analytic functions

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11 Citations (Scopus)

Abstract

Let Hμ (double-struck D sign) be the weighted Banach space of analytic functions with a topology generated by weighted sup-norm. In the present article, we investigate the analytic mappings φ1*phi;2:double-struck D sign → double-struck D sign and θ π : double-struck D sign → ℂ which characterize the compactness of differences of two weighted composition operators Wφ1,θ -Wφ2,π on the space Hμ (double-struck D sign) . As a consequence we characterize the compactness of differences of composition operators on weighted Bloch spaces.

Original languageEnglish
Pages (from-to)419-428
Number of pages10
JournalIntegral Equations and Operator Theory
Volume62
Issue number3
DOIs
Publication statusPublished - Nov 2008

Fingerprint

Weighted Composition Operator
Space of Analytic Functions
Banach space
Compactness
Bloch Space
H-space
Composition Operator
Weighted Spaces
Topology
Norm

Keywords

  • Compact oerator
  • Weighted Banach space of analytic functions
  • Weighted composition operator
  • Weighted sup-norm

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Analysis

Cite this

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AB - Let Hμ∞ (double-struck D sign) be the weighted Banach space of analytic functions with a topology generated by weighted sup-norm. In the present article, we investigate the analytic mappings φ1*phi;2:double-struck D sign → double-struck D sign and θ π : double-struck D sign → ℂ which characterize the compactness of differences of two weighted composition operators Wφ1,θ -Wφ2,π on the space Hμ∞ (double-struck D sign) . As a consequence we characterize the compactness of differences of composition operators on weighted Bloch spaces.

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KW - Weighted composition operator

KW - Weighted sup-norm

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