Banach–Stone theorems for algebras of holomorphic germs on spaces with the approximation property

Daniela M. Vieira

Mathematische Nachrichten, 2023, vol. 296, issue 11, 5070-5076

Abstract: It is shown that if K⊂E$K\subset E$ and L⊂F$L\subset F$ are balanced compact determining subsets of separable Banach spaces with the approximation property, then the algebras of holomorphic germs H(K)$\mathcal {H}(K)$ and H(L)$\mathcal {H}(L)$ are topologically algebra isomorphic if, and only if, K̂P(E)$\hat{K}_{\mathcal {P}(E)}$ and L̂P(F)$\hat{L}_{\mathcal {P}(F)}$ (the polynomial convex hulls of K and L) are biholomorphically equivalent.

Date: 2023
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https://doi.org/10.1002/mana.202200245

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