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<p>We introduce the concept of vector-valued holomorphic mappings on the complex unit disk that factor through a Hilbert space and state the main properties of the space formed by such Bloch mappings equipped with a natural norm: linearization, Bloch transposition, surjective and injective Banach ideal property, Kwapień-type characterization by Bloch domination, and duality.</p>

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Factorization of Bloch mappings through a Hilbert space

  • 期刊论文

  • 发表日期：

    2025年1月24日

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  • M. G. Cabrera-Padilla,
  • A. Jiménez-Vargas,
  • D. Ruiz-Casternado

摘要

We introduce the concept of vector-valued holomorphic mappings on the complex unit disk that factor through a Hilbert space and state the main properties of the space formed by such Bloch mappings equipped with a natural norm: linearization, Bloch transposition, surjective and injective Banach ideal property, Kwapień-type characterization by Bloch domination, and duality.