Vol. 65, No. 2, 1976

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A characterization of Riemann algebras

Bruno Kramm

Vol. 65 (1976), No. 2, 393–397

A topological algebra 𝒜 is called Riemann algebra if it is topologically isomorphic to the Fréchet algebra 𝒪(R) of all holomorphic functions on some Riemann surface R.

One obtains a characterization of Riemann algebras by a theorem of R. L. Carpenter and the Oka-Weil-Cartan theorem; we show that: a uniform Fréchet algebra 𝒜 whose spectrum is locally compact and connected, is a Riemann algebra if and only if every closed maximal ideal is principal.

Mathematical Subject Classification 2000
Primary: 46J15
Received: 28 January 1976
Revised: 15 June 1976
Published: 1 August 1976
Bruno Kramm