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A distance formula and Bourgain algebras

Published online by Cambridge University Press:  24 October 2008

R. Younis  and
D. Zheng
R. Younis
Affiliation:
Department of Mathematics and Computer Science, United Arab Emirates University, P.O. Box 17551, Al Ain, United Arab Emirates
D. Zheng
Affiliation:
Department of Mathematics, Michigan State University, East Lansing, MI 48824†
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Abstract

In this paper, a distance formula to a Douglas algebra is established. We use this distance formula to show that the distance of an L∞ function to the intersection of arbitrary Douglas algebras is equivalent to the supremum of the distance of that function to these algebras. As an application, we prove that the Bourgain algebra of the intersection of two Douglas algebras is equal to the intersection of the Bourgain algebras of these two algebras.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 120 , Issue 4 , November 1996 , pp. 631 - 641
Copyright
Copyright © Cambridge Philosophical Society 1996

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References

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