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Interpolation sets for convolution measure algebras


Author: Colin C. Graham
Journal: Proc. Amer. Math. Soc. 38 (1973), 512-522
MSC: Primary 43A10
DOI: https://doi.org/10.1090/S0002-9939-1973-0318778-8
MathSciNet review: 0318778
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Abstract: These are proved: (1) The union of two interpolation sets for a regular commutative convolution measure algebra is not necessarily an interpolation set. (2) There exists a regular commutative convolution measure algebra for which interpolation sets are not necessarily of spectral synthesis, while every singleton is a Ditkin set. (3) For every nondiscrete LCA group $ G$, there exist compact interpolation sets for $ M(G)$ whose union is not an interpolation set. A tensor algebra method is used.


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DOI: https://doi.org/10.1090/S0002-9939-1973-0318778-8
Keywords: Convolution measure algebras, interpolation set, Helson set
Article copyright: © Copyright 1973 American Mathematical Society

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