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Boundaries for polydisc algebras in infinite dimensions

Published online by Cambridge University Press:  24 October 2008

J. Globevnik
J. Globevnik
Affiliation:
University of Ljubljana
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Abstract

Let AB be the algebra of all bounded continuous functions on the closed unit ball B of c0, analytic on the open unit ball, with sup norm, and let AU be the sub-algebra of AB of those functions which are uniformly continuous on B. Call a set S ⊂ B a boundary of AB (AU) if

for every f ∈ AB (f ∈AU, respectively). In the paper we study the boundaries of AB and AU. We give a complete description of the boundaries of AU and present some necessary and some sufficient conditions for a set to be a boundary of AB. We also give some examples of boundaries.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 85 , Issue 2 , March 1979 , pp. 291 - 303
Copyright
Copyright © Cambridge Philosophical Society 1979

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References

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