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At the crossroads of holomorphic dynamic and operator theory: spectral properties of composition operators on
$\mathrm {Hol}(\mathbb {B}_N)$
- Part of
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- Journal:
- Canadian Mathematical Bulletin , First View
- Published online by Cambridge University Press:
- 11 June 2025, pp. 1-26
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- Article
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We study the class of composition operators acting on the Fréchet space
$\mathrm {Hol}(\mathbb {B}_N)$ of all holomorphic maps on the unit ball of 
$\mathbb {C}^N$. We describe the conditions to make these operators continuous, invertible and compact. We also do the spectral study of these operators, depending on the nature of its symbol.
