ALGEBRAS ON SURFACES

The first part of the paper is devoted to algebras on one-dimensional varieties in Cn that are bounded by finite unions of mutually disjoint rectifiable simple closed curves. The relevant Shilov boundaries are considered, and certain nonapproximation phenomena are exhibited. The second part of the p...

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Bibliographic Details
Published in:Mathematica scandinavica 2015-01, Vol.116 (1), p.104-125
Main Author: STOUT, EDGAR LEE
Format: Article
Language:English
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Summary:The first part of the paper is devoted to algebras on one-dimensional varieties in Cn that are bounded by finite unions of mutually disjoint rectifiable simple closed curves. The relevant Shilov boundaries are considered, and certain nonapproximation phenomena are exhibited. The second part of the paper is devoted to the study of uniform algebras whose maximal ideal spaces are smooth surfaces and that admit sets of smooth generators. Such algebras are shown to consist of functions holomorphic off their Shilov boundaries.
ISSN:0025-5521
1903-1807
DOI:10.7146/math.scand.a-20453