Vol. 43, No. 2, 1972

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Interpolation sets for uniform algebras

Arne Stray

Vol. 43 (1972), No. 2, 525–529

Let A be a uniform algebra on a compact Hausdorff space X and let E X be a closed subset which is a Gδ. Denote by BE all functions on XE which are uniform limits on compact subsets of XE of bounded sequences from A. It is proved that a relatively closed subset S of XE is an interpolation set and an intersection of peak sets for BE if and only if each compact subset of S has the same property w.r.t. A. In some special cases the interpolation sets for BE are characterized in a similar way. A method for constructing infinite interpolation sets for A and BE whenever x E is a peak point for A in the closure of X∖{x}, is presented.

Mathematical Subject Classification 2000
Primary: 46J10
Received: 26 July 1971
Revised: 22 September 1971
Published: 1 November 1972
Arne Stray
Mathematics Institute
University of Bergen
5007 Bergen