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Norm preserving interpolation sets for polydisc algebras

Published online by Cambridge University Press:  24 October 2008

Josep Globevnik
Josep Globevnik
Affiliation:
E.K. University of Ljubljana, Yugoslavia
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Abstract

Let N > 1 and let AN be the polydisc algebra, i.e. the algebra of all continuous functions on the closed polydisc δ¯N ⊂ N, analytic on the open polydisc δN, with sup norm. Call a closed set F ⊂ δ¯N a peak interpolation set for AN if given any f ε C(F), f ≠ 0, there is an extension f ε AN of f such that ¦f˜(z)¦ < ‖ f ‖ (z ε δ¯N - F); call F a norm preserving interpolation set for AN if given any f ε C(F) there is an extension f˜ ε AN of f such that ‖f˜‖ = ‖f‖. The paper gives a complete description of norm preserving interpolation sets for AN in terms of peak interpolation sets for AM, M ≤ N.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 91 , Issue 2 , March 1982 , pp. 291 - 303
Copyright
Copyright © Cambridge Philosophical Society 1982

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References

REFERENCES

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