Compact multipliers on spaces of analytic functions

Paweł Mleczko

Compact multipliers on spaces of analytic functions

Functional Analysis 2008-08-12 v1 Complex Variables

Authors: Paweł Mleczko

Abstract

In the paper compact multiplier operators on Banach spaces of analytic functions on the unit disk with the range in Banach sequence lattices are studied. If the domain space $X$ is such that $H_\infty\hookrightarrow X\hookrightarrow H_1$ , necessary and sufficient conditions for compactness are presented. Moreover, the calculation of the Hausdorff measure of noncompactness for diagonal operators between Banach sequence lattices is applied to obtaining the characterization of compact multipliers in case the domain space $X$ satisfies $H_\infty\hookrightarrow X\hookrightarrow H_2$ .

Keywords

compact multipliers analytic functions Banach spaces sequence lattices Hausdorff measure of noncompactness diagonal operators

Cite

@article{arxiv.0808.1359,
  title  = {Compact multipliers on spaces of analytic functions},
  author = {Paweł Mleczko},
  journal= {arXiv preprint arXiv:0808.1359},
  year   = {2008}
}

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