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A note on weighted Banach spaces of holomorphic functions. (English) Zbl 1047.46018
The authors deal with weighted spaces of holomorphic functions. Let $G$ be an open subset of ${\Bbb C}^N$ and $v: G \to {\Bbb R}$ a continuous, strictly positive function, called a weight. Then the main result of the paper states that $$(Hv)_0(G) = \{ f: G \to {\Bbb C} :\ f \text{ holomorphic, } v\vert f\vert \text{ vanishes at } \infty \}$$ endowed with the weighted sup-norm $$\Vert f\Vert _v = \sup_{z \in G } v(z) \vert f(z)\vert$$ is always isomorphic to a subspace of $c_0$. This was previously known only for very restricted classes of weights and open sets $G$.

46E15Banach spaces of continuous, differentiable or analytic functions
46B03Isomorphic theory (including renorming) of Banach spaces
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