The Cesàro Operator in Growth Banach Spaces of Analytic Functions
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- 作者：Angela A. Albanese ; José Bonet ; Werner J. Ricker
- 关键词：Cesàro operator ; growth Banach space of analytic functions ; mean ergodic operator ; optimal domain
- 刊名：Integral Equations and Operator Theory
- 出版年：2016
- 出版时间：September 2016
- 年：2016
- 卷：86
- 期：1
- 页码：97-112
- 全文大小：627 KB
- 刊物类别：Mathematics and Statistics
- 刊物主题：Mathematics
Analysis - 出版者：Birkh盲user Basel
- ISSN：1420-8989
- 卷排序：86
文摘
The Cesàro operator C, when acting in the classical growth Banach spaces \({A^{-\gamma}}\) and \({A_0^{-\gamma}}\), for \({\gamma} > 0\), of analytic functions on \({\mathbb{D}}\), is investigated. Based on a detailed knowledge of their spectra (due to A. Aleman and A.-M. Persson) we are able to determine the norms of these operators precisely. It is then possible to characterize the mean ergodic and related properties of C acting in these spaces. In addition, we determine the largest Banach space of analytic functions on \({\mathbb{D}}\) which C maps into \({A^{-\gamma}}\) (resp. into \({A_0^{-\gamma}}\)); this optimal domain space always contains \({A^{-\gamma}}\) (resp. \({A_0^{-\gamma}}\)) as a proper subspace.