Uniform Fréchet algebras with prescribed endomorphism group (Q1205487)

A topological algebra is a Stein algebra if there exists a Stein space \(X\) such that it is topologically and algebraically isomorphic to \({\mathcal O}(X)\), the algebra of all holomorphic functions on \(X\). The problem of characterizing Stein algebras has generated much energy. One approach to this problem is to study uniform Fréchet algebras. It turned out that in many cases such algebras are Stein algebras. Singly generated reflexive \(uF\)-algebras with connected spectrum are isomorphic to \(\mathbb{C}\), \(O(D)\) or \(O(\mathbb{C})\). Additional hypotheses are given to derive an analogous result for \(n\)-generated \(uF\)-algebras \((n>1)\).