Unimodular Möbius-Invariant Contractive Divisors for the Bergman Space

Abstract

Let B be a Banach space of analytic functions in the open unit disk D. For a sequence {α_ν} (α_ν ∈D) let

$$ {B_{\left\{ {{\alpha_v}} \right\}}} = \left\{ {{\text{f}} \in B} \right.|{\text{f}}\left( {{\alpha_v}} \right) = 0,\forall v $$

((1))

(repeated values of αν correspond to multiple zeros of f). {α_ν} is called a B-zero set if B{α_ν} ≠}0}.

To Israel Gohberg with affection and admiration.