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Spectrum of Compact Weighted Composition Operators on the Weighted Hardy Space in the Unit Ball

Abstract

Let be the unit ball in the-dimensional complex space, for, a holomorphic function in, and, a holomorphic map from into itself, the weighted composition operator on the weighted Hardy space is given by, where. This paper discusses the spectrum of when it is compact on a certain class of weighted Hardy spaces and when the composition map has only one fixed point inside the unit ball.

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Correspondence to Ze-Hua Zhou.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Zhou, ZH., Yuan, C. Spectrum of Compact Weighted Composition Operators on the Weighted Hardy Space in the Unit Ball. J Inequal Appl 2007, 061313 (2007). https://doi.org/10.1155/2007/61313

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Keywords

  • Holomorphic Function
  • Unit Ball
  • Hardy Space
  • Complex Space
  • Composition Operator
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