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Montel Algebras on the Plane

Published online by Cambridge University Press:  20 November 2018

W. E. Meyers
W. E. Meyers*
Affiliation:
The University of British Columbia, Vancouver, British Columbia
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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).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 22 , Issue 1 , 01 February 1970 , pp. 116 - 122
Copyright
Copyright © Canadian Mathematical Society 1970

References

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