A+ CATEGORY SCIENTIFIC UNIT

Lineability of the set of holomorphic mappings with dense range

Volume 210 / 2012

Jerónimo López-Salazar Studia Mathematica 210 (2012), 177-188 MSC: Primary 46G20; Secondary 46E50. DOI: 10.4064/sm210-2-5

Abstract

Let $U$ be an open subset of a separable Banach space. Let $\mathcal{F}$ be the collection of all holomorphic mappings $f$ from the open unit disc $\mathbb{D}\subset \mathbb{C}$ into $U$ such that $f( \mathbb{D}) $ is dense in $U$. We prove the lineability and density of $\mathcal{F}$ in appropriate spaces for different choices of $U$.

Authors

  • Jerónimo López-SalazarDepartamento de Análisis Matemático
    Universidad Complutense de Madrid
    28040 Madrid, Spain
    e-mail

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