Abstract
We prove that two domains of holomorphy U and V in separable Frechet spaces with the bounded approximation property are biholomorphically equivalent if and only if the topological algebras (H(U);?) and (H(V );?) are topologically isomor- phic for ? = ?0; ?!; ?-. We prove also that given two absolutely convex open subsets U and V of Tsirelson-like spaces, the algebras of holomorphic functions of bounded type Hb(U) and Hb(V ) are topologically isomorphic if and only if there is a biholo- morphic mapping of a special type between U and V. We obtain similar results for algebras of holomorphic germs H(K) and H(L), where K and L are two compact subsets of Tsirelson-like spaces.
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