Geodesic
Montel Algebras on the Plane
Canadian journal of mathematics, Tome 22 (1970) no. 1, pp. 116-122

Voir la notice de l'article provenant de la source Cambridge University Press

The results of Rudin in [7] show that under certain conditions, the maximum modulus principle characterizes the algebra A (G) of functions analytic on an open subset G of the plane C (see below). In [2], Birtel obtained a characterization of A(C) in terms of the Liouville theorem; he proved that every singly generated F-algebra of continuous functions on C which contains no non-constant bounded functions is isomorphic to A(C) in the compact-open topology. In this paper we show that the Montel property of the topological algebra A (G) also characterizes it. In particular, any Montel algebra A of continuous complex-valued functions on G which contains the polynomials and has continuous homomorphism space M (A) homeomorphic to G is precisely A(G). 
Meyers, W. E. Montel Algebras on the Plane. Canadian journal of mathematics, Tome 22 (1970) no. 1, pp. 116-122. doi: 10.4153/CJM-1970-014-5
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